1500

IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 Soft Robotics: Morphology and Morphology-inspired Motion Strategy Fan Xu, Stdent Member, IEEE and Hesheng Wang, Senior Member, IEEE

Abstract—Robotics has aroused huge attention since the 1950s. interaction between robots, human beings, as well as the Irrespective of the uniqueness that industrial applications exhibit, environment. It has also been known for its ability to conventional rigid robots have displayed noticeable limitations, particularly in safe cooperation as well as with environmental eliminate the unintentional collision and impact with the adaption. Accordingly, scientists have shifted their focus on soft coexistence between robots and humans. Conversely, robotics to apply this type of robots more effectively in conventional rigid robots have displayed significant unstructured environments. For decades, they have been limitations in addressing this issue [1], [2]. Several committed to exploring sub-fields of soft robotics (e.g., cutting- comprehensive review papers have been published [3]; edge techniques in design and fabrication, accurate modeling, as well as advanced control algorithms). Although scientists have moreover, several narrative review papers have been made, made many different efforts, they share the common goal of primarily reviewing fabrication [4] and actuation methods enhancing applicability. The presented paper aims to brief the (e.g., fluid-driven actuation [5], [6], shape memory alloy progress of soft robotic research for readers interested in this (SMA) [7], dielectric elastomer-based actuation (DEA) [8], field, and clarify how an appropriate control algorithm can be produced for soft robots with specific morphologies. This paper, [9], granular jamming actuation [10], actuation for small-scale instead of enumerating existing modeling or control methods of a robots [11]), control algorithms [12], and applications (e.g., certain soft robot prototype, interprets for the relationship biomedical use [13]–[15], biomimicry [16], [17]). between morphology and morphology-dependent motion strategy, In contrast with the mentioned review papers, this paper attempts to delve into the common issues in a particular class of aims to develop a framework to determine how to soft robots, and elucidates a generic solution to enhance their performance. mathematically model a type of soft robot prototypes; subsequently, we discuss appropriate control algorithms based Index Terms—Soft continuum manipulator, soft gripper, soft mobile robot, soft robot control method, soft robot modeling method, on the specific morphology and characteristic of this congener soft robotics. to enable the soft robot to perform in target control tasks. In

this regard, we delve into the underlying principle of the I. Introduction motion of most existing soft robots that follow different HE term of “soft robotics” is primarily defined as an mechanisms to clarify a strategy to unify modeling, sensing, Tautonomous system with rigid mechanism and flexible and control methods into a certain type of soft robot for joints that exhibits passive compliance, or a system made from readers interested in relevant fields. To this end, the paper low modulus materials, characterized by inherent compliance enumerates typical morphologies and configurations of from elastic/hyper-elastic materials. In this paper, the latter existing soft robots, and then presents unified technologies of definition is highlighted to present the progress in this area, modeling, sensing and control algorithms with typical cases. which covers the advanced modeling and control methods that Hopefully, this paper can outline feasible methods according have been practically applied in non-industrial environments. to different morphologies and tackle common issues facing Soft robotics is considered a novel branch of robotics, which the respective type of soft robot. is an intersection of multiple disciplines, e.g., biology, chemistry, electromechanics, and electrochemistry, etc. It has It is known that soft robots made of compliant materials generated rising interest for its potential to induce seamless outclass traditional rigid robots in cooperation and coexistence with humans, undertaking tasks without being given absolute Manuscript received February 20, 2021; revised April 9, 2021; accepted May 7, 2021. Recommended by Associate Editor Long Chen. (Corresponding environment information, locomotion in rough terrains, etc. author: Hesheng Wang.) They are also known to be advantageous for their capacity in Citation: F. Xu and H. S. Wang, “Soft robotics: Morphology and tasks that rigid robots cannot deal with [18]. For the morphology-inspired motion strategy,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1500–1522, Sept. 2021. mentioned properties, soft robotics is considered a solution The authors are with the Department of Automation, Institute of Medical that boosts the evolution of robots in unstructured Robotics, Key Laboratory of System Control and Information Processing of environments [2]. In the meantime, however, challenges Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: [email protected]; [email protected]). facing the actual implementation of soft robots are generated, H. S. Wang is also with the Key Laboratory of Marine Intelligent which can be summarized into four aspects in the relevant Equipment and System of Ministry of Education, Shanghai Jiao Tong scientific literature [3]: University, Shanghai 200240, China. 1) Fabrication of its unique mechanism; Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. 2) Accurate mathematical model of the system; Digital Object Identifier 10.1109/JAS.2021.1004105 3) Intrinsic sensing device that can be utilized for the XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1501 deformable mechanism; routines), soft-bodied robots demonstrate more flexibility in 4) Real-time control algorithm to ensure vigorous deformation; besides bending and twisting, they are performance. sometimes also capable of stretching and contraction when Over decades researchers have committed to the soft adopting pneumatic actuator. Due to better deformability, soft robotics related branches (e.g., advanced material continuum robots exhibit better shape adaptability but are not investigation, smart actuator design, compliant sensing device satisfying in load capacity or stiffness. A comparison between development, modeling, and control [19]–[22]) to terminally these two types of robots is given in Table I. enhance the performance of soft robot system. In the following, several common types of soft robots will A. Morphology be exemplified, and corresponding modeling and control Invertebrates, exemplified by the octopus, are characterized strategies that are feasible for such specific types are by impressive dexterity and vigorous grasping behavior, even elaborated to provide a new researcher with an intuitive though they do not have a spine. Researchers have been framework. Biology (e.g., human beings) is commonly interested in exploring its structure, neural system and the considered to be highly adaptable to uncertain environments underlying principles of sensorimotor control to reproduce for their high-level sensing systems and sensorimotor control. their powerful behaviors on the robot platform. Other than Researchers have fixed their concentration on biology to find investigating whole invertebrates, some researchers have something that can be implemented into soft robots. To this concentrated on investigating invertebrates’ appendages. end, by reviewing numerous studies, it is found that existing Octopus tentacles, demonstrating large-ratio extension and soft robots usually engage in similar morphology and motion contraction ability, can squeeze themselves into a highly modes with living biology. Prevalent morphologies usually constrained environment, reach and fetch the object rapidly adopted in soft robot systems will be enumerated. Three types during predation. Soft continuum robots that are based on the of soft robots are reviewed, which include the soft continuum morphology of octopus tentacles, trunk and other analogous robot (Section II), soft gripper (Section III), and soft mobile morphologies of the living organism, are one of the primary robot (Section IV). Each section exemplifies the current types of soft robots and have been continuously growing over progress on modeling and control methods and ends with a the past decades. We will exemplify studies of soft continuum short discussion. Section V summarizes this paper and robots, except for those that are rigid ones, in this section. provides a conclusion of the existing approaches, technical Biologists have reported on the special structure of limitations and potential study trends in the domain of soft invertebrates that enables their powerful sensorimotor robots. The outline is demonstrated in Fig.1. abilities, which is the mechanism composed of muscular hydrostats. Such structure shows astonishingly accurate controllability of each piece of muscular tissue to support Soft continuum robot (Section II) ● Morphology diverse motions (e.g., elongation for reaching, contraction for ● Modeling squeezing into a small room, as well as omnidirectional ● Control bending for dexterous behavior). The studies on the ● Discussion Conclusion characteristics of such unique tissue that enable distinct Soft robot & Soft gripper (Section III) performance have long been conducted [23]–[26]. Though the (Section I) Discussion ● Morphology (Section V) theoretical model to describe the motion of octopus tentacles ● Modeling & Control is developed, such motion is yet unlikely to be thoroughly ● Discussion reproduced in a robot system. Difficulties may originate from Soft mobile robot (Section IV) several limitations of techniques in its development include ● Morphology the design of controller to mimic the neural system, feasible ● Modeling & Control sensing devices to provide considerable environmental ● Discussion information, etc. In brief, there remains a gap between the

Fig. 1. Outline of the structure. theoretical analysis of biomechanics and how it is adopted in the robot systems to reproduce the identical advanced and II. Soft Continuum Robot intelligent sensorimotor control. The breakthroughs of soft A soft continuum robot can be considered as the intersection robotic techniques require multi-discipline contributions. of a soft robots and continuum robots. Continuum robotics has Numerous research has presented soft robot prototypes that become a flourishing research area with various work on its exhibit analogous morphologies to mechanisms of living design, modeling, control, and applications. Partial continuum biology. In many publications, different mechanism designs to robots are made of rigid materials, distinguished by a higher mimic the shape and function of the octopus tentacle young’s modulus as well as higher inherent stiffness [3]; yet [26]–[31] and trunk [32]–[39] have been found. Figs. 2 and 3 soft continuum robots are more compliant and characterized demonstrate several soft continuum robot prototypes. The by continuous deformability of their backbone, thereby proposed robot prototypes permit a motion pattern that can exhibiting infinite degrees of freedom. Compared to rigid perform bending [28], [40]–[47], and sometimes elongating continuum robots which are usually actuated by embedded and contracting motions [26], [29], [32]–[39], [48]–[51]. In tendons and can achieve bending and twisting deformation [46], a soft manipulator outfitted with a pneumatic actuation (the latter depends on the accommodations of tendon method is fabricated and employed in a grasp-and-place task 1502 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

TABLE I Comparison in Rigid Continuum Robot and Soft Continuum Robot

Item Rigid continuum robot Soft continuum robot Dimensionality Infinite Infinite Actuator Continuum (commonly adopt tendon-driven actuator) Continuum (diverse actuators) Characteristics Deformability Bending, twisting Stretching, contraction, bending, twisting,... Stains/deflection Small Large Material selection Shape memory alloy Rubber, polymers, ... Accuracy High Low Load ability Lower Lowest Security level Low High Flexibility High High Working condition Unstructured environment Unstructured environment Capacity Objective requirement Variant size Variant size Compatibility with obstacle Good Best Controllability Low Low Path planning Hard Hard Location detection Hard Hard Inspiration resource Skeleton Muscle

appropriately regulating the synergy motion of these bellow- like chambers. In [30], EGaIn-based soft sensors are integrated with the pneumatically-actuated soft robotic manipulator to acquire the motion state and enable vigorous grasping. It is noteworthy that the time delay and hysteresis may be caused during pressurization and vacuum process, and the (a) (b) control performance will be consequently degraded. Such effect can be reduced by the presented parallel-accommodated Section 2 Vacuum independent actuator [32], [33]. A similar actuation method

Endplate Elongation sensor has been extensively adopted in existing studies [34]–[39]. Air in Other fluid-driven soft continuum robots, as presented in Section 3 Bending actuator Expansion sensor several studies [48], [54], have been deeply investigated in Base Suction cup terms of their modeling and control strategy. Similar morphology of an octopus tentacle or trunk can also be found

Section 1 in [28], [50], [55]–[58]. A silicone-made cable-driven soft (c) (d) robot manipulator is cast into a similar shape with an octopus tentacle. Omnidirectional bending performance can be Fig. 2. Soft continuum robot prototypes inspired from octopus tentacle. (a) achieved by pulling the embedded cables to regulate the 12-cable-driven soft robot arm [27] (Copyright © 2014, IEEE); (b) Bio- orientation of bending as well as the bending angle. Maghooa inspired manipulator with hybrid tendon and pressure actuation [28] et al. [28] presented an octopus-inspired soft manipulator (Copyright © 2015, IEEE); (c) OctArm V [29] (Copyright © 2008, IEEE); using a hybrid actuation method. The proposed prototype is (d) Pneumatically actuated soft robotic tentacle with integrated strain sensors characterized by multi-bending performance, as enabled by [30] (Copyright © 2020, IEEE). regulating tendon displacement, and variant stiffness under pressurization and depressurization of the pneumatic actuator. by adopting open-loop control strategies. A similar A similar actuation method was also adopted in [59] to obtain mechanical structure of this manipulator has also been double functions of both accurate positioning and adjustable employed in several publications [40], [41], [48]. A redundant stiffness. Such hybrid actuation methods have been proved to octopus-like soft robot manipulator is presented in [29], [31], be feasible to actively control the stiffness to achieve a wider [52], [53], consisting of three pneumatically actuated sections range of load capacity [60]. accommodated in cascade. Each of the sections is composed of three parallel-accommodated chambers with periphery fiber B. Modeling for Soft Continuum Robot to constrain the expansion radially and enable unidirectional In this section, we review commonly adopted kinematic and extension axially. Accordingly, the bending and elongation dynamic modeling methods and summarize their performance of the manipulator can be obtained by characteristics in Table II. XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1503

and revolute joints in their depiction of configuration space.

Section 1 On the whole, this method is built on the hypothesis that the 200 mm Vicon tracker shape of the backbone after its deformation can be considered to consist of sequential arcs, each of which exhibits invariant Section 2 200 mm curvature. Subsequently, the spatial configuration parameters are then defined to depict the curve of the backbone in the Markers form of the shape consisting of cascaded arcs. When a continuum backbone is thought to meet the constant curvature (a) (b) assumption, the modified Denavit-Hartenberg (DH) convention can be computed based on arc geometry. Frenet frame is introduced to describe such a quasi-circular shape in the robot configuration space based on artificially defined generalized coordinates. Thus, one can compute local transformation between two adjacent robot sections and then express the forward kinematics abiding by the chain rule. This method is well accepted in modeling congeneric soft continuum robots with planar or spatial motion [26], [28], [36], [40], [42]–[49]. Recently, it has been verified that this (c) (d) method can also be used to model the self-growing soft robot

[63]. The modeling method based on constant curvature Fig. 3. Soft continuum robot prototypes inspired from trunk. (a) Festo’s assumption is known as an analytical solution since it leads to Bionic Handling Assistant with pneumatically actuated bellows [34] an explicit expression of the system kinematics, thereby (Copyright © 2017, IEEE); (b) Pneumatically actuated soft manipulator with contributing to model-based control. Despite the reinforcement learning closed-loop control [51] (Copyright © 2019, IEEE); demonstration of potential and feasibility to the employment (c) Pneumatic muscle based continuum robot with embedded tendons [32] in closed-loop controller design, it is argued to be less (Copyright © 2018, IEEE); (d) Trunk-like arm with 12 fluid actuators and 12 accurate especially when external loads are applied on the soft proprioceptive sensors [58] (Copyright © 2020, IEEE). robot. In such cases, the section will not remain the same curvature. This can be addressed by adopting variable 1) Kinematics curvature assumption [33], [34], [36], [37], [56]. By Soft continuum robot manipulators display similar discretizing the continuum backbone into multiple virtual mechanical properties to rigid continuum robots that consist of sections, each virtual section can then be considered to permit cascaded rigid joints, which have aroused increasing attention a constant curvature while a variable curvature is compared over decades [61]. Researchers have delved into their with that of its adjoining virtual section. By enhancing the mechanism and motion pattern and have also committed to discretization of the soft continuum robot, the constant- accurately modeling the system and designing closed-loop curvature constraints can be maintained in each virtual controllers to enable the robot a better applicability. Despite subsection and the model accuracy will be optimized in the different characteristics between rigid and soft continuum comparison with the physical model. This modeling method robots, the analogous principle of motion of both is assumed can generally depict the circular-like configuration of a soft (as listed in Table I). In this view, the modeling and continuum robot and construct the mapping, findependent, of the controlling methods can be considered versatile in these two configuration space and Cartesian space, while specific domains. Thus, the modeling methods studied in domains of mapping, fspecific, of the actuation space and configuration both rigid and soft continuum robots have been reviewed. As space should be solved. For instance, when the tendon-driving a result, benefiting from similar kinematics, modeling work is actuation method is adopted, the configuration parameters, tractable by referring to the modeling method of a rigid which are arc length, orientation angle and curvature radius, continuum robot. The universal modeling and control method can be functioned with respect to tendon variables [56], and in a continuum robot will be reviewed here whether it is made the forward kinematic mapping fspecific can be consequently from a soft or rigid material. Unlike conventional rigid robots constructed. The kinematics from the actuation space to the with articulated prismatic and revolute joints, those soft robots Cartesian space can be obtained by combining fspecific with are characterized by continuous deformability along the findependent, as seen in Table II. backbone at an arbitrary position. Hence, they are considered Besides analytical solutions to kinematics by as systems with infinite degrees of freedom (DOFs) in the mathematically modeling the system, numerous studies also configuration space. In most cases, it is assumed that soft focused on numerical modeling methods and model-learning robots exhibit a hyper redundant mechanism that permits high techniques to solve system forward and inverse kinematics but finite DOFs when being kinematically modeled. [64]. [65] presented a framework of kinematic modeling There is a method adopted extensively to model this type of method for continuum robots using the modal approach, robot manipulator, which is the so-called constant-curvature where the spatial curve shape of the continuum robot was based kinematic modeling method [62]. Such a method depicted in terms of the polynomial function. Digumarti et al. differentiates that of conventional rigid robots with prismatic [66] have also employed shape function to model the shape of 1504 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

TABLE II Modeling Strategies for Soft Robots and Their Properties

Mathematical modeling Computer-aid modeling Data-driven modeling Lumped-parameter modeling Distributed-parameter modeling Method Neural network-based model Constant curvature assumption-based Elastic rod theory-based FEM learning

Sketch 50 KPa

45 KPa 20 KPa 35 KPa

Applying Usually in a regular-shape soft Usually in a regular-shape soft Versatile in robots even with Versatile in robots even with object continuum robot continuum robot an irregular shape an irregular shape Underlying Equilibriums of Equilibriums of energy/momentum / System identification with principle energy/momentum/forces forces Equilibriums of statics neural network architecture • Available ODEs form of motion equations • Comparatively high accuracy to • Viable for all types of soft • Viable for all types of soft Pros • Closed-form solution constant curvature assumption- robots robots • Desirable in control based method • Strong assumption in configuration space • PDEs-form motion equations, lack- • Lack of explicit solution • Tedious and time-consu- • Degrading accuracy in high deflec- ing analytical solution • High-dimension equations ming data collection and tion • High computation load required to be solved in each offline model training Cons • Constrained use dependent on robot • Constrained use dependent on robot iteration • Lack of analytical solution configuration configuration • Challenges in real-time appli- • Sometimes suffers from • Nonlinearity in actuators enhancing • Nonlinearity in actuators enhancing cation under/over fitting, degrad- modeling complexity modeling complexity ation in performance

the continuum robot and express the configuration in the form parameters should be updated based on the strain analysis, of Fourier’s series. By using such a method to model a with given force conditions. Hence, to accurately model the continuum robot, numerical optimization methods are usually system in the situation with existing external loads or adopted to solve the curve-fitting problem and determine the interactive effects, the variance of kinematic parameters specific shape function best approximating the spatial curve of caused by imposed forces and torques should be highlighted, a continuum robot. Modeling learning methods have been and a feasible way should be developed to eliminate their studied, contributing to learning-based open-loop control [51], effects. To this end, the coupling mechanical properties should [64], [67]–[73]. To learn an accurate system model, be studied to achieve more sophisticated and accurate system considerable motion data of system input and corresponding model. Researchers have been committed to the study of output have been collected to span the training set. Obviously, statics [52], [55], [74]–[76] and dynamics [27], [50], [54], the accuracy is highly dependent of the feasibility of the [77]–[82] of the continuum soft robot. It is known as a training set. Goal babbling method is proved to be viable in prerequisite to enable a force control strategy or acceleration- generating sufficient training data and addressing the based control strategy. By discretizing the continuum robot multiple-solution problem in inverse kinematics of the hyper into multiple virtual sections, the motion of each of them can redundant manipulator [69]. The obtained inverse kinematics be considered to integrate several prismatic and revolute rigid of the presented soft robot then illustrates its accuracy in robot links accommodated sequentially. Accordingly, subject point-to-point open-loop control tasks. to constant curvature or variable curvature assumption, 2) Statics and Dynamics dynamic modeling methods for conventional rigid robots with Kinematics is subject to increasing errors in the situation articulated joints can also be verified in continuum robots. The with unneglectable external loads and environmental contacts. Lagrangian formulation and Euler-Newton equation, which Unlike rigid robots, soft robots demonstrate strong coupling are among the most frequently adopted methods in modeling between kinematics and statics/dynamics owing to the rigid robotics, are also feasible in this case. It is noted that deformability of their compliant mechanism, making it less kinematics is a prerequisite under which the position and accurate to express the motion with respect to given position velocity of the center of mass can be computed. Afterwards, signals as actuation inputs. In such scenarios, the the mechanics or statics of each virtual section can be configuration is determined by the input position signal as formulated based on force, momentum or energy equilibrium. well as the external force/torques. To be more specific, the By combining all equilibriums for each discrete virtual variable geometric parameters (e.g., length of the link) due to section, a normalized form of system mechanics or statics is applied forces/torques will be obtained, and then, kinematic obtained. The internal energy change due to the deformation XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1505 of the mechanism should be considered. It can be modeled velocity, acceleration, and external wrench. Note that the based on the constitutive law of materials characterized by linear and angular strain can be formulated as a partial hyperelasticity or viscoelasticity [83]. Marchese et al. [40] differential of the position vector and Euler angle with respect presented a discrete modeling method to express the dynamics to arc length, while the velocity and acceleration exhibit a of the pneumatic soft manipulator in a similar shape to trunk. differential and doubly differential form with respect to time. This method is also known as an analytical method to model Accordingly, by solving the set of PDEs numerically, robot the system since the closed-loop form of motion equations can configuration at arbitrary position can be obtained along the be obtained this way. Next, the solved model proved its continuum robot backbone. Trivedi et al. [29] have developed accuracy in open-loop point-to-point control tasks. A similar a geometrically exact model based on the Cosserat rod theory analytical method has been extensively adopted in soft for the soft robot manipulator, OctArm V. The model exhibits continuum robots. Reference [54] presented a discrete method high accuracy even if a large deformation of the robot is to model the system leveraging the Lagrange formulation. The observed, given consideration to nonlinear strain model. presented soft robot arm was in a similar shape to that in [40] Though they present the dynamic equations in their study, the consisting of three cascade sections, each of which has three validation concentrates on the static case. Renda et al. [77] independent bellow-like chambers. The motion of this also leveraged Cosserat rod theory to model system dynamics manipulator is obtained by the generated longitude force from of an octopus-tentacle-like soft manipulator. In their paper, a pressurization of each bellow. The specific bending and general method was proposed to model the system dynamics elongation performance can be achieved by appropriately of the congener of cable/tendon-driven soft continuum robots. adjusting the length of each chamber. In their studies, the Unlike that of fluid-driven soft robots aforementioned [29], actuation space inputs, which are pressures generated by the they additionally considered the contact along the air pump, can be accurately mapped to the robot motion of cable/tendon path as evenly distributed force and modeled in bending and elongation in work space. Thus, the performance line with centripetal force [73]. Subsequently, they extended of positioning and tracking can be achieved by regulating the the system dynamics into an underwater environment by input pressure to obtained reference force driving actuators to further considering hydrodynamics [27]. Dynamic modeling deform to the desired pose. Nevertheless, it is argued that such work on congeneric cable/tendon-driven continuum robots can a method shows constraints in situations where external also be found in [78], where external loads were considered. forces, e.g., gravity, contacts, etc., exist and enhance the While the continuum methods are reported to be more configuration coupling effect. In the mentioned scenarios, the accurate in modeling the system motion equation under a perfect circular shape hardly permits pure bending motion large deformation or deflection, it is subject to the high hardly permits. Thus, augmented generalized coordinates are computation load hindering the implementation in real-time defined to better capture the spatial shape of a continuum control. This is because there is no explicit expression of the robot with torsion and contraction along its backbone [50], Jacobian matrix, and its numerical solution requires tedious [84]. This modeling method has also proved its feasibility in iterative computation and extra work to solve the boundary aquatic environments where fluid interactions are considered and initial conditions. To this end, Rucker et al. [88] proposed [80] to extend its application into underwater environments a feasible way to calculate the Jacobian when modeling the [85]. system with a numerical method, in the scenario with external Apart from the aforementioned analytical solutions based on loads. To enhance the ability of real-time computing, the discretization assumption, numerical solutions based on researchers have contributed to improving computation continuum methods, are also comprehensively studied. efficiency. Till et al. [89] first presented the system dynamics Continuum methods originate from beam theory, which is of the continuum robot based on Cosserat rod theory and then considered a branch of solid mechanics and exemplified by proposed a real-time computing method to the numerical Cosserat rod theory for the spatial-motion case and Euler- solution to the model based on time discretization. Bernoulli beam theory planar-motion case. Highly coupled Accordingly, the problem was simplified to find the solution partial differential equations (PDEs) construct the distributed- of ordinary differential equations (ODEs) every time step. parameter model and depict the motion of a continuous curve Giorelli et al. [72] further investigated the solution to inverse in the Frenet-Serret frame. The statics can be expressed as a statics based on the iteratively solved Jacobian for a planar- set of ordinary differential equations where the variables are motion soft robot. Subsequently, they verified its accuracy by considered time-invariant, while dynamic motion equations implementing it into a feedforward force control. Finite comply with the rule represented by PDEs where the variables element model (FEM)-based methods also require real-time are both space- and time-variant. To better understand the computing for solving the updated node positions in every underlying principle of this method, interested readers can time step. In primary cases, system statics are modeled based refer to [52], [53], [86], [87]. The continuum method is on the force equilibrium. Solving the compliance matrix is characterized by better handling of the coupling between considered the critical point to this modeling method [90], kinematic parameters and applied loads. The stress analysis is [91], based on which the displacement of actuator and the formulated on the infinitesimal segment, and is assumed to be system states can be computed by given external forces. rigid. Given the constitutive law of elastic or viscoelastic Considering the coupling effect, FEM-based method can material, the linear strain and angular strain can be modeled enable a position control performance [92]. Recently, into the expression consisting of terms of the linear/angular Grazioso et al. [93] demonstrated a unified method to solve 1506 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 system dynamics, inverse kinematics and differential unknown parameters of friction, and then optimized the kinematics by combining the Cosserat rod theory with the parameters by minimizing the mismatch in measured and helical shape function based FEM. computed tendon variables, as well as input forces. A learning-based method is reported as a feasible method to Furthermore, the extension of the cable/tendon due to robotic modeling and control without any pre-knowledge of a elasticity also results in inaccuracy. Camarillo et al. [100] robot system. Researchers have studied the implementation of presented unified mechanics that consider such effects. neural networks in soft robot modeling work [71], [72]. In the Subsequently, the model was implemented in the tracking task study, the inverse statics learning method was developed in robot configuration space [101]. Therein, reference tendon based on a feed-forward neural network. Subsequently, open- inputs were computable if given the desired configuration loop control was adopted to validate the model performance in with a solved system model. For soft continuum robots with the two-dimensional positioning task. Despite the advanced materials as their actuators (e.g., SMA [7], DEA [8], simplification in mathematical modeling work, model- [9], etc.), unneglectable hysteresis phenomena shall generate learning methods cannot permit feedback control due to interest. Researchers tend to adopt mathematical models to paucity of an analytical solution to the Jacobian that can compensate for nonlinear hysteresis effects (e.g., Preisach accurately build the map between the robot actuation space model [102], Prandtl–Ishlinskii model [103], etc.) to further and workspace. It is known that with the existence of a reduce modeling error and to enhance performance in control Jacobian matrix, the reference inputs can be computed as per [104]. Here we only present clues for different mathematical the measured states and output feedback respective sampling modeling methods to solve hysteresis rather than provided time. For the system adopting model learning method, little detailed explanations of them. For more information,

knowledge on how kinematic and dynamic parameters affect interested readers can refer to the reviewed paper preceding. the system performance is available, making it difficult to iteratively modify the inputs according to the error feedback. C. Control Strategies for Soft Continuum Robot Therefore, model learning methods have usually been With the solved system model, a specifically designed employed in open-loop control tasks, the accuracy of which is controller can enable desired performance of a soft robot in highly dependent on the training process. These methods certain tasks. Usually, closed-loop control is preferable to an result in no solution to address possible modeling errors that open-loop strategy in positioning and tracking tasks requiring can be done in the case of closed-loop control with knowledge high accuracy. In this section, we review existing control of the system. Consequently, in such system, the divergence strategies of soft robots and summarize their characteristics, of output error is hard to theoretically prove to warrant system strengths/weakness in Table III, followed by sketches of stability. Besides the case of closed-loop control-mentioned control architectures (including model-based kinematic/static general modeling methods, specific characteristics (resulting control (Fig. 4), dynamic control (Fig. 5), and model-less control (Fig. 6)) and open-loop control architecture (Fig. 7). from different actuators, materials, and configurations) should 1) Kinematic/static Control also be considered. An accurate model to depict deformation It is known that the analytical solution of a system model is required. There are numerous mathematical methods that can contribute to a closed-loop control algorithm with contribute to modeling nonlinear materials with the appropriate selection of different intrinsic or exterior sensors characteristics of elasticity, hyperelasticity or viscoelasticity. that can provide shape [105]–[110], position [48], [111], To be specific, the Ogden model, the Yeoh model, and the [112], tactile and other feedback information [113], [114]. Polynomial model are frequently employed in modeling the Palmer et al. [115] demonstrated the model-based stress and strain [83], [94], [95]. For instance, the Neo- configuration trajectory tracking performance of a continuum Hookean model was adopted in [29] to formulate the robot with a similar shape to a snake. In their study, shape constitutive relation of the material and model the nonlinear tracking control and end effector positioning were axial strain energy. The cable/tendon-driven actuation method simultaneously permitted. Gilbert et al. [116] investigated a exhibits compactness, rapid and stable force-transmission, similar problem in the case where pre-curvatures exist and the which has been well studied and extensively employed in realized leader-following motion synchronizes with insertion medical and surgery use [96]. Despite the fact that this method into constrained terrain. Their studies further enhanced the has its benefits, it suffers from unneglectable friction along the potentials of a continuum robot in the application of in vivo tendon path, degrading accuracy in the control task if no navigation in minimally invasive surgery [117], [118]. A solution is created to address these issues. Though such effect graphical measurement system is known for its high economy can, to some extent, be mitigated by properly designing and its ability to provide considerable environmental sleeves, which can enclose the embedded cable/tendon and information. It has been broadly employed for shape sensing avoid direct contact between the cable/tendon and the soft [105] and visual servoing control [85], [112], [119]. robot, the friction effect remains and causes a loss in Researchers have studied vision-based control and have been transmission force along the cable/tendon path [97]. committed to specific problems. To solve the unknown Subramani et al. [98] proposed a mathematical model to camera mapping between the image space and robot inputs express the friction effect in a congeneric cable/tendon-driven with an uncalibrated camera, Fang et al. [119] proposed an continuum robot. It is also reported that such an effect could online method to solve the camera model based on Gaussian be compensated by model-based parameter identification. Roy process regression, and enabled the soft robot to execute et al. [99] assumed an exactly known model of statics with positioning and tracking tasks. Uncalibrated problem can also XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1507

TABLE III Control Methods for Soft Robot

Closed-loop Method Model-based Model-based Model-less: Model-less: Open-loop Kinematic/static control Dynamic control Learning-based Jacobian estimation Commonly adopted in simple movement (the Summary Desirable in control tasks with high-demanding accuracy control of soft gripper and soft mobile robot)

Sensing ... techniques Soft electronics (optical fiber, membrane, ), vision-based, self-sensing based on advanced materials, model-based shape and force sensing Sketch Fig. 4 Fig. 5 Fig. 6 Fig. 6 Fig. 7 • Easier mathematical modeling work than• Suggested control strate- dynamic control gies given considerations • Circumventing the dif- • Better real-time com- of special mechanism• Circumventing the diffi- ficulties in mathema-• Easy to realize with iden- Pros putation characteristics culties in mathematically tically modeling nonli- tified mechanics/ statics • Comparatively easier • Able to accelerate the mo- modeling nonlinearity nearity architecture than dyn- vement and to control amic control the dynamic response • Modeling inaccuracy/ • Modeling inaccuracy/ • Low frequency (output uncertainties degrade the uncertainties degrade the feedback-based optimi- performance performance • Performance depends on zation) • Highly dependent on mo- Cons • Less accuracy in dyna- • High computation load the trained model • Decreased accuracy in deling accuracy mically interactive envir- resulting from modeling high-speed motion (ext- • Comparatively large error onment complexity ended Kalman Filter)

yd y Kinematic/static Controls τ Learning-based Δ Soft robot + controller Learned inverse Offline model − y kinematics/statics training Actuation space Task space Inverse kinematics/statics feedback y · d Δy Model-less Controls feedback y or Jacobian transpose q, q τ Soft robot Task space + controller feedback y − y

Jˆ Actuation space Fig. 4. Block diagram of closed-loop kinematic/static control. feedback, q q· Estimated Jacobian J e.g., Kalman filter,

y q, q· optimization method Jacobian estimation yd Dynamic Controls τ Δy + Soft robot + controller − y + Fig. 6. Block diagram of (model learning-based (top) and Jacobian estimation-based (bottom)) model-less control. Actuation space Nonlinear dynamics feedback compensation term q, q· Task space yd Known system Controls feedback y Soft robot model τ

Fig. 5. Block diagram of closed-loop dynamic control. Fig. 7. Block diagram of open-loop control. be addressed using adaptive method [85], [120]. In these of contact that causes part of the cable-driven robot to be studies, online estimation laws were designed to update locked, after which the kinematic model can be updated. Yip unknown camera parameters. Appropriate control algorithms et al. [129] presented an optimization-based method to were also proposed to enable kinematic visual servoing iteratively solve the Jacobian matrix online by minimizing the control [120], [121] as well as dynamic visual servoing task space error and enabled two-dimensional positioning tracking control [85]. It is known that kinematic controllers control in the environment with obstacles. Motion control are highly restricted to control tasks with environmental with contact was also studied in [130]–[132], where the interactions. The mapping between a configuration space and contact model was introduced to map the external wrench in actuation space will be less accurate due to uncertain task space to the reference displacement based on interactive effects, including the contact with the external environment stiffness. Li et al. [32] presented a model-less environment, unmeasurable forces exerted on the system, and method to cope with the modeling inaccuracy. In their study, other disturbances. To this end, interaction controllability is they treated entries in the Jacobian matrix as system states and also analyzed in continuum robots [39], [120], [122]–[129]. estimated them using the adaptive Kalman filter. Thus, the An adaptive visual servoing controller was proposed in [120]. Jacobian matrix could be solved without dependency on pre- Therein, the proposed adaptive law can estimate the location knowledge of the system model but was subject to the 1508 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 constraints at the small perturbation assumptions during each accuracy of modeling of these two mappings. Researchers sampling time. The extended Kalman filter is also reported to have suggested several methods to improve modeling be feasible in shape estimation [133]. Ataka et al. [134] accuracy. Parameter identification is presented to compute the proposed an obstacle-avoiding method. The repulsive force unknown system coefficients [155]. The constants in the was modeled inspired from electromagnetic effect and was mechanics of the pump used to pressurize the chambers were used to guide the continuum robot away from obstacles. solvable. Then, a backstepping control algorithm was Meanwhile, point-to-point control of its end effector could be employed to generate reference inputs of fluid actuators with realized. This method differentiates from other obstacle- given measurements in the robot task space. In several studies, avoiding methods in that it requires no pre-knowledge of the similar methods of model-based parameter identification were environment [135]. adopted [42], [54], [155], [156]. It is noteworthy that with the solved kinematics, statics or dynamics of the robot, the shape [136]–[138], external loads D. Discussion on Soft Continuum Robot [139]–[146], and contact [147]–[150] are intrinsically It is worth noting that in this section we review several estimable, enhancing the ability of a continuum robot to publications presenting continuum robots with rigid parts, the interact with surroundings by optimizing its perception ability major topics of which are solutions to modeling and control in the absence of bulky forces or tactile sensors. Over the past problems. Due to similar morphology and similar motion several years, numerous research has been conducted principles, the methods are considered universal in these two concerning contact detection and localization. Bajo et al. domains. The level of study on rigid continuum robots is more [148] proposed a novel kinematic-based framework for mature. Thus, researchers can solve common issues by collision detection by monitoring the screw motion deviation, referring to existing studies on rigid continuum robots and fixed centrode deviation, as well as joint force deviation considering typical problems raised by specific characteristics [149]. Several studies have combined shape information and of soft robots. the kinematic/static model to estimate external forces. Xu Soft continuum robots are usually endowed with a simple et al. [141] proposed a solution of model-based estimation of mechanism, making their motions predictable from a the external load acting on the robot end effector with mathematical aspect; thus, numerous studies concentrate on measured input tension on driven tendons. In the paper, the the real-time modeling and control methods. Despite diverse kinematics was obtained by solving arc geometry, and the actuation methods adoptable, e.g., fluid-driven, tendon-driven, statics was formulated based on the principle of conservation SMA-based actuation methods and so forth, a similar circular- of energy. With the solved Jacobian matrix and ascertained shape motion mode of a soft continuum robot can be cable tensions, the unknown external load could be easily achieved, making it possible to use a unified method to computed. Khoshnam et al. [139], [150] also proposed a construct the mapping between the configuration space and shape-based force estimation method to solve the force the task space, and to mathematically model system motion sensing problem in applications of minimally invasive surgery equations. Discretization of the continuum mechanism is one and biopsy. Fiber-Bragg-gratings (FBG) sensor is one of a of the commonly employed strategies, based on which feasible way to provide shape information [143]. Other studies lumped-parameter model can be established. The model then on force estimation method based on system statics are fully serves as a basis for model-based controller design. The investigated in [144]–[146]. Apart from the aforementioned kinematics and dynamics based on this idea have a closed- methods, Roy et al. [142] further studied the dynamics of the form solution similar to that of a traditional rigid robot. As system and derived the external force expression with the shown in Table II, the sketch is given under the classification consideration of dynamic effects. Interaction controllers of lumped-parameter modeling, demonstrating the unified [122]–[124], ensuring compliance of the robot with respect to discrete method to depict the circular shape in the the environment, were then developed leveraging intrinsic configuration space. The lumped-parameter model has better force measuring method. real-time computing capacity and shows better control- 2) Dynamic Control oriented ability than the distributed-parameter model, which is Model-based closed-loop control strategies can generally solved based on continuum method leveraging the elastic rod achieve trajectory tracking performance in the task space with theory (as shown in Table II). Yet the former suffers from analytically solved dynamics of the system [34], [47], [50], relatively high modeling errors/ uncertainties to the continuum [51], [80], [151], [152]. Trajectory tracking performance was modeling method, FEM, and model-learning method, obtained based on solved system dynamics using an open-loop implying that error compensation measures should be taken in control strategy [153], as well as following a closed-loop the upcoming controller design to avoid degrading image-based visual servoing control strategy [154]. Note that performance. Soft continuum robots usually enjoy regular for the dynamic control of a fluid-driven soft robot, there are morphology and are endowed with high-level adaptability to usually two-stage controllers required, namely the bottom the surroundings. Hitherto many studies have focused on motion controller that maps the outputs in task space to the theoretical modeling and control methodology. Nevertheless, reference inputs in robot joint space, and the upper-level one unsolved issues that hinder powerful execution in real that computes the controls in actuation space based on the applications still exist, demanding more intensive study. For joint space reference, respectively. Hence, the accuracy of the instance, an unfathomed paradox between the level of proposed control algorithm is highly dependent on the accuracy and real-time computing ability in modeling and XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1509 control remains unsettled. In addition, despite progress in both many open solutions. It is acknowledged that in terms of an kinematic and dynamic control, limited work concentrates on industrial robot hand, a pre-knowledge of the objects is one of interaction or force control problems. What’s more, this type the prerequisites in grasping tasks to solve the planning of soft robot features higher degrees of freedom in its problem and obtain a feasible grasping pose that can result in configuration space than in the actuation and task space; thus robust grasping behavior. Soft grippers demonstrate it can be regarded as a redundant system (from configuration superiority compared with rigid robot grippers, especially in space to task space) and underactuated system (from actuation that they enjoy better shape adaptability, significantly space to configuration space). This uniqueness obviously simplifying the grasping process by eliminating the detection generates challenges in control tasks. A high-performance of objects. Several typical soft gripper prototypes are shown in controller should simultaneously cope with difficulties coming Fig. 8. Soft robot grippers possess diverse morphologies, from both underactuated and overactuated systems, e.g., the operate by leveraging advanced soft actuators, and are null-space control problem in an underactuated system and endowed with dexterity from their bio-inspired mechanism redundancy allocation in an overactuated system, etc. Despite design and sometimes intrinsic sensing ability [157]–[177]. In numerous control strategies that have been described, few of particular, they outclass rigid robot grippers in manipulation them pinpoint this issue. tasks with fragile objects [178], [179]. Interestingly, there is an overlap between soft continuum robots and soft grippers, III. Soft Gripper implying that similar modeling methods used in soft Soft robots are uniquely qualified for manipulation tasks continuum robots can be adopted in soft grippers. Note that involving fragile objects, with which rigid robots are not when referring to the terminology of a gripper, we assume that competent. There is a large role for grasping with rigid a gripper sometimes includes the mechanical design of grippers in the industrial environment. However, rigid multiple fingers, each of which usually permits continuum grippers display constraints in daily applications, where the requirement of safe manipulation without damaging the object properties. In this light, the difference between this section hinders its implementation in subtle manipulation tasks. A and the previous section is that in the study of grippers, considerable number of methods are proposed for rigid emphasis will be laid on the synergy motion strategy rather gripper control. Visual classification of the objects after which than the specific motion of a single continuum soft finger. suitable grasping poses are determined is one of the most The human hand can perform vigorous grasping because of conventional methods that have been reported in numerous its mechanism that combines the structure of a clamping

publications. It is a necessity for a rigid gripper to obtain an optimized grasping pose and act at the appropriate position on the object according to its center of mass. During its operation, a point-contact model is usually developed in the task, which should be carefully analyzed to ensure a force closure for successful grasping. To be specific, rigid grippers demonstrate superiority in industrial applications due to their high precision and load capacity produced by program-by- teaching motion and high-gain control loop. Conversely, these grippers lose flexibility and compliance in unstructured environments where human-machine interaction exists. Soft (a) (b) graspers, in contrast to their rigid counterpart, perform vigorous grasping without any requirement for pre-knowledge of the object shape. Heuristically, face or line contact, usually generated in soft gripper operation, can achieve more robust grasping performance since such contact can easily form a force closure, which is a prerequisite for a successful grasp. A soft gripper outperforms its rigid counterpart in dexterity and safety when executing tasks in daily applications due to its shape adaptability inherent from its compliant mechanism. Most existing publications specialize in novel designs that guarantee robust grasping performance. Theoretical system models of the reported soft gripper prototypes are seldom (c) (d) (e) possibly attributing to the common metrics in a task not being the accuracy but the completeness of a grasping motion. Fig. 8. Soft gripper prototypes. (a) Soft robotic gripper with passive particle Instead, data-based and unsupervised learning methods are jamming [157] (Copyright © 2017, IEEE); (b) The pneumatically-actuated implemented to fulfill a specified task. The following section RBO Hand 2 manipulating an abacus [158] (Copyright © 2016, IEEE); (c) A universal gripper based on the jamming [159] (Copyright © 2012, IEEE); (d) will review the common types of soft robot grippers. A gecko elastomer actuator gripper [160] (Copyright © 2018, IEEE); (e) A 3- A. Morphology D-printed soft gripper with suction cup for effective grasping [161] (Copyright © 2019, IEEE). The study of soft gripper continues to be ongoing with 1510 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 component (multiple fingers) and a sustaining component effect refers to another well-known example in bionic design. (palm) [164]. Its mechanism and motion pattern have been This comes from the configuration and mechanism of a fish well studied and considered to be an excellent example fin. Engineers have been inspired by this effect to design a inspiring the design of robot grippers. There are many flexible grasper, adapting to the shape of objects and fabrication methods with different actuators adopted to permit performing vigorous grasps [180], [181]. A granular jamming similar morphology and thus replicate the similar motion based gripper is also well investigated this decade [159], pattern of a human hand with a robot gripper [158], [171]–[176]. These robot prototypes show versatile grasping [165]–[169]. Pneumatic actuators have been extensively ability of various objects with a simple control strategy, applied in the design and fabrication of soft grippers for the leveraging good shape adaptability inherent from their shape adaptability and controllable stiffness, both desirable for mechanism and good load capacity based on a vacuum

dexterous and vigorous grasping [158], [165]–[167], [177]. process. Deimel et al. [158] designed and fabricated a pneumatically actuated anthropomorphic soft robot gripper. With five fingers B. Modeling and Control Strategies for Soft Gripper that can perform grasping posture and one pad serving as a Rare studies have focused on theoretical dynamic modeling supporting part, the presented prototype demonstrated the of soft grippers. The coordination motion pattern enhances ability of dexterous and tight grasping of objects. It also coupling inside the mechanism, thereby increasing complexity exhibited good capacity of manipulation with objects with of mathematical modeling work. A wide range of publications high weight, the performance of which was validated in have presented open-loop and learning-based methods for multiple grasping tasks. Nagase et al. [166] presented a grasping control [161,] [165], [169], [176], [182], [183] similar design in their study that emphasized variable stiffness (referring to Table III). It is argued that vigorous grasping can of robot fingers to overcome contradictory demand be realized by leveraging passive compliance even without an specifications regarding both dexterous manipulation and accurate contact model, instead of a traditional closed-loop vigorous grasping of diverse objects. Ilievski et al. [163] control strategy with force feedback loop. Researchers have presented a gripper with a similar shape to a starfish, actuated concentrated on upper-level control to plan a task-oriented by a Pneumatic Networks (PneuNet) based elastomer. The motion sequence and provide accurate performance with grasping-and-place behavior can be achieved by pressurizing given excitations [169], [182], while bottom motion control the fingers to bend them inward and depressurizing them to can be achieved by following learning-from-demonstration recover their initial shapes. Nassour et al. [177] demonstrated strategy or simple open-loop control strategy. Amend et al. an integral design of the soft gripper, where curvature and [176] presented a gripper with two jamming actuators, each of pressure sensors were mounted on pneumatically-actuated which are treated as a robot finger, oppositely accommodated fingers to enhance interactive capabilities with the external on the palm to clamp an object with combined action from environment and assess the shape information of both the vacuum suction. In their study, the authors analyzed the gripper and object. Besides pneumatic actuators, smart effective grasping force generated from friction and vacuum materials also make a soft gripper functional. SMA-based process although they gave no clues on how this could be actuators have been well studied. In [168], a soft robot hand utilized into the controller design. Tawk et al. [161] also that can imitate similar gripping performance of a human hand presented a teleoperated three-finger gripper unified with a was proposed. The presented soft robot hand achieves bending suction pad to provide high load capacity. Force analysis was performance by actuating embedded SMA strips sticking to developed to model its payload in finger grasping and suction the internal side of five silicone-made fingers. A similar behavior. Faria et al. [183] proposed a learning-based method design can be found in other studies. Wang et al. [170] for the presented pneumatically-actuated soft robot hand. In presented a SMA-based robot hand with three fingers, each of their study, the prototype was trained to imitate the which can achieve unidirectional bending performance. Two demonstration of a human hand and replicate grasping hinges on each finger can noticeably change stiffness, given performance. Similarly, Gupta et al. [165] enabled the soft the requirements of a grasping force in specific tasks. Nasab et hand to perform grasping through learning and imitating from al. [179] also demonstrated a method to change the stiffness, human manipulation. leveraging hybrid pneumatic actuator and elastomer strips. C. Discussion on Soft Gripper The presented gripper can be controlled with its grasping behavior of each finger being pneumatically actuated to Soft grippers provide good grasping performance with facile perform bending. Lower and higher stiffness can be obtained control strategies. A soft gripper can circumvent the planning by, respectively, heating up and cooling down the elastomer of a grasping pose thanks to its shape adaptability that can strips incorporated with the pneumatic actuator. Manti et al. easily ensure the force closure. Safe grasping manipulation is [167] adopted a simplified design principle in their study, guaranteed without complex force control architecture due to where three paralleled accommodated fingers were unified for its compliant mechanism. These merits enable increased grasping tasks. Grasping behavior is realized when fingers investigation of this type of soft robot, especially when it simultaneously bend inward, with actively changed lengths of comes to the manipulation of fragile objects. The morphology embedded cables. Bending performance can be achieved by is essential to the performance of a soft gripper, while it driving one motor to control all three cable variables, demands joint contributions of advanced actuation methods employing a synergetic motion control strategy and open-loop ensuring rapid response and an optimized mechanism design control units, with no requirements for sensing. The fin ray providing vigorous grasping action. Compliance is the XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1511

dominant property that enables desirable shape adaption and allows a soft gripper to have safe interactions without meticulous design of the controller, while at the same time decreasing the load capacity of the prototype. One should take into account this trade-off while considering specific demands of the task when integrating the material and corresponding mechanical design techniques. This issue is especially challenging when subtle manipulation is required, e.g., in- hand manipulation. Better manipulation performance requires active shape and force regulation. This can be realized with (a) (b) embedded strain and tactile sensors. However, though numerous soft grippers have been proposed, few studies Morphing concentrate on in-hand manipulation. Commonly adopted structure 3D printed underactuated mechanical systems additionally increase the soft leg Rigid complexity of manipulation controller design. Ongoing frame Textured foot (for friction) research concentrating on integration technology of material, mechanics and control would further enhance the application 5 cm 15 mm Bottom view in real manipulation tasks in diverse environments. (c) (d)

IV. Soft Mobile Robot Fig. 9. Exemplified underwater soft mobile robot prototypes. (a) Octopus- Mobility and navigation in diverse terrains have long been like robot capable of swimming [184] (Copyright © 2018, IEEE); (b) studied to enhance the versatility of robots in multiple Leptocephali-inspired soft robot with dielectric elastomer actuators [185] scenarios. Untethered soft robots operating in various (Copyright © 2018, IEEE); (c) Soft modular swimming robot with oscillating environments have generated increasing interest in this fins [186] (Copyright © 2020, IEEE); (d) Soft underwater walking robot with decade. It is acknowledged that soft robots ensure prominent active flow adaption by changing the shape [187] (Copyright © 2019, IEEE). environmental adaptability due to their morphologies and bio- inspired sensorimotor control patterns. Researchers have been organisms have long inspired researchers to do mechanical inspired by living organisms that survive after long-term design (as shown in Fig. 9) and study motion control method evolution and show transcendence in adaption to particular of underwater robots. The octopus, an example of marine habitats. Multiple studies and reports can be found. Numerous invertebrate, features good performance in underwater soft robot prototypes that mimic the locomotion of their environments. Known for its abilities to squeeze itself into a biological counterparts exist, exhibiting eminence when highly constrained environment, the octopus performs rapid operating in specific working environments. The mechanical and accurate reaching and fetching movement during its design of existing bio-inspired soft mobile robots demon- predation, and executes biped motion in the seabed. Thus, strates a strong correlation with the environment. Figs. 9–11 researchers have delved into the underlying principle of its give several examples of the soft mobile robots. motion achieved by its unique morphology, aiming to reproduce such advanced performance in a robot platform. A. Morphology Octopus-inspired soft robots that mimic the swimming and To be the fittest in natural selection, biological organisms gait of their biological counterpart are studied. It is known that continue to optimize their morphologies to specific habitats in a robot exhibiting a similar shape to living organisms is more generation-by-generation evolution and are eventually likely to intimate their locomotion. The bio-mimetic endowed with good morphology and sensorimotor mechanical design of underwater soft robots inspired by the capabilities. Researchers are inclined to fabricate a soft robot octopus has been presented in [184]. The prototype displays a prototype with similar morphology to the living organisms so spheroid shape of its major body with eight soft arms evenly that the robot can reproduce their motion patterns and distributed at its underside periphery. Other studies demonstrate distinct performance in specific conditions. concentrating on octopus-inspired soft robots investigated the Therefore, soft robots demonstrate various morphological design method as well as locomotion strategies [188]–[190], characteristics, differentiated by their potential work [195]. The presented prototypes demonstrate both crawling environments. Subsequently, the paper will examine soft [188], [189] and swimming [184], [190], [195] performance mobile robots by exemplifying typical types of commonly by learning motion patterns from its biological counterpart. adopted morphology and motion strategies that enable them On the whole, these motions are realized by coordination good mobility in target territories. motion control of multiple soft arms rather than jet propulsion 1) Underwater Bio-inspired Soft Mobile Robot methods that were studied in [191], [192], [196]. It is well Several studies have been primarily discussing on known that underwater environments impose extra underwater bio-inspired robot design and locomotion disturbances on aquatic robotic systems. When a robot strategies enabled by soft actuators [16], e.g., legged operates in such a situation, further study should be conducted locomotion [184], [187]–[190], jet propulsion [191]–[193], to eliminate enhanced external interactions applied by the undulating motion [185], [186], [194], etc. Marine living surrounding fluid. Otherwise, performance will be degraded, 1512 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 or the system can even collapse. In contrast, the specific strategies that are unified to obtain the impressive mobility in underwater environment is conducive to some locomotion unstructured environments even if with complex terrains (as strategies. From the perspective of actuation, the underwater shown in Fig. 10). Several studies exist with the aim of environment facilitates the operation of a specific type of replicating such performance in robot platforms [202]. A actuator. Liu et al. [194] presented a design of a propulsion snake-like soft robot prototype was proposed in [203] and use device in a similar shape to the fish fin. The locomotion slithering locomotion while leveraging friction of its contact performance of the proposed prototype was tested underwater, surface. and its effectiveness in generating propelling force was shown. Meanwhile, the energy cost required for the generation t = 0 of motion was minimized. Another instance is the ionic polymer metal composites (IPMC)-based actuation method, of which the working principle is ion motion with an applied external voltage differential. The external electrodes generate t = T/4 attractive and repulsive forces, thereby causing non-uniform distribution of ions based on the principle of “opposite attraction.” Subsequently, the deformation can then be achieved due to the difference in qualities of anthode and cathode. This actuator is capable of more effectively operating t = T/2 in aquatic environments, since moisture on electrodes in underwater environments can facilitate free motion of ions (b) [16]. The aquatic environment is also known for enhancing t = 3T/4 Body Soft Pneumatic agility by narrowing the cooling time for an actuator based on Actuator tether temperature-induced phase change, e.g., SMA. To this end, z y numerous prototypes have been developed leveraging these x advanced-material actuators. With bio-inspired morphologies, (c) several soft mobile robots are fabricated with similar motion t = T patterns relative to their biology counterparts. It is acknowledged that IPMC- and SMA-based actuation methods lead to soft robotic mobility generated by in-turn undulation motion of fin-like or tail-like mechanisms [16]. The (a) (d) undulating or oscillating motion can also be generated by employing this actuation method. Unlike the motion strategies Fig. 10. Exemplified on-the-ground bio-inspired soft mobile robot based on fin actuation, jet-propelled actuation, inspired by the prototypes. (a) Fluid-driven soft robot permits inchworm crawling [197] motion pattern of sepia, is analyzed as well to perform a rapid (Copyright © 2020, IEEE); (b) An inchworm-inspired soft robot capable of movement in aquatic environments [191], [193]. omega-arching locomotion [204] (Copyright © 2017, IEEE); (c) A legged soft 2) On-the-ground Bio-inspired Soft Mobile Robot robot capable of navigating unstructured terrain [198] (Copyright © 2017, In addition to robots working in aquatic environments, IEEE); (d) A soft robot with wall-climbing ability enabled by electroadhesive researchers have also been inspired by biological foot [205] (Copyright © 2018, IEEE). morphologies (e.g., multi-arms) that enable robust motion mode in rough terrains [197], [198]. Some researchers argue There is a universally adopted method of mechanical design that the optimized performance of a soft robot cannot be of caterpillar-inspired and earthworm-inspired soft mobile achieved with artificial and heuristical mechanical and robots. That is, the architecture of the robot displays the controller design. Instead, it should evolve its mechanism, combination of two connection parts and one core body part. motion pattern, as well as control algorithm with predefined During the operation, deformation, either extension/ target environments and specific tasks to eliminate “designers contraction or bending, of the core body part enables stride- bias” [199], [200]. Corucci et al. [201] presented a self- like motion with given periodic excitations based on the evolutionary theory for a soft robot through simulation, to actively changing body length. In the meantime, one prove its feasibility in the design of morphology and connection anchors to the environment, and the other moves locomotion strategy for a bio-inspired soft robot with multiple with its core body part. This peristalsis-like forward or legs. Thus far, such a theory has not been reported in practical backward movement can then be achieved by regulating the applications. action sequence that consists of the motions of three parts. The study of motion patterns of the earthworm, caterpillar The deformability of the core body part is critical to varying and other annelids has long been conducted. These organisms body length. In this light, researchers have studied the demonstrate agile and robust locomotion in various terrains, characteristics of different actuators to enhance the by leveraging their soft architectures to execute sequential deformation effectiveness and agility. Soft actuators, namely contraction and extension motions of their body for forward, SMA-based actuators [7], [206]–[210], electroactive polymer backward, and turning movement. Researchers, therefore, are (EAP)-based actuators [9], [205], electromagnetic actuator inspired by the biomechanics as well as their locomotion [211], [212], and pneumatic actuators [204], [213]–[216] are XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1513 implemented in soft robot systems which can then reproduce the period of input signal sequence. The undulation motion the motion pattern accordingly. Existing soft mobile robots pattern has been adopted in several studies [208], [217], [221], following peristaltic motion patterns usually have similar [222]. Wang et al. [221] presented a pneumatically-actuated morphology to that of an annelid. To achieve periodic body- earthworm-like soft robot. Bending performance was obtained length variation of the robot, researchers combine elastic through pressurization of the chambers linearly distributed materials with smart soft actuation methods to mimic undulate along its core body part. The in-turn anchoring behavior of the or stretching behavior inspired by their biology counterparts. front and backend of the robot was achieved by passive The function of the connection part that is to fix/disconnect friction-changing ability. In their study, the front and backend the robot to the contact can be realized by actively sheet-like parts were designed to permit a certain angle enhancing/reducing the friction [204], [205], [208]–[210], relative to the baseboard to change the contact area in [217]–[219]. According to an alternative strategy, the different motion phases. Such a method has been commonly interchanging fixing and disconnection to the current contact employed in the mechanical design work of earthworm- can be achieved by a gripping and loosing action enabled by a inspired soft robots [193], [208], [217], [222]. unified gripper system [213]. The functions of these 3) Miniaturized and Micronized Soft Mobile Robot connecting and flex parts are unified in a feasible manner to Miniaturized and micronized soft robots have aroused permit forward, backward, and turning behaviors. They can increasing attention recently. Fig.11 demonstrates several then underpin applications in navigation and locomotion into instances of small-scale soft mobile robots. The mobility in multiple environments. A viable way to actively adjust the highly constrained environments endows it with potentials in friction is to change the area of contact interface. Ge et al. diverse applications [223]–[225], including drug delivery in [217] presented the design and fabrication work of a medical use [226], [227], and subtle manipulation with cells in pneumatically actuated soft robot. In their study, the fiber bioengineering use [228]. reinforcement accommodation was adopted to constrain the performance of the actuator to be unidirectionally stretched → → 1.7 cm HA HA Permanent sagittal plane along the axial direction. Subsequently, the stride-based magnet Frontal plane motion was then obtained by pressurizing or depressurizing its Front 1.7 cm T = 0 s Transverse plane T = 0 s core body part, with joint contribution from connection parts. Holding Front cage Pivot corners Mountain fold (bottom) Valley fold The anchoring to the contact of either the upfront or rear part 1 s 4 s was achieved by increasing the static friction in the contact Walking Swimming B B interface, through pressurization-based expansion. Similar 2 s 8 s working principles can be found in a tube-climbing robot 4 s 13 s [220]. The presented robot prototype adopts the pneumatic 5 mm (a) actuation method as well. Accordingly, the performance of 5 s 20 s Silver wires to anchoring to the tube can be obtained by selectively feedback sensory Silver wires connect (c) data ① ② sensors and pressurizing the top or bottom part. Alcaide et al. [219] also Pneumatic microprocessor tubes presented a soft robot that can perform both rectilinear Silver wires climbing motion and turning behaviors. The robot consists of to provide power Microprocessor three cascade sections, each of which is made of silicone and Liquid metal Leading 10 mm ③ ④ edge is actuated with three embedded parallel-accommodated SMA 15° strings. The radial expansion, to fix the robot inside the tube, (b) (d) and shape recovery, to obtain body length variable by Fig. 11. Exemplified miniaturized and micronized soft mobile robot reverting the core body from expanded to normal shape, can be achieved, respectively, by simultaneously heating and prototypes. (a) A magnet-driven origami robot capable of walking and cooling all three SMA strings embedded in one section. swimming [229] (Copyright © 2015, IEEE); (b) SMP-made four-limb soft ro- Bending behavior can be achieved by partially actuating SMA bot with self-sensing ability [230] (Copyright © 2020, IEEE); (c) Magneti- strings in one section to change the orientation in the cally actuated microrobot with integrated tail and body morphology [231] locomotion. Rozen-Levy et al. [213] demonstrated a unified (Copyright © 2016, Huang et al); (d) RUBIC [232] (Copyright © 2019, Chen, et al). design of the gripper system and core body. In the study, the contraction and shape recovery can be, respectively, achieved Hu et al. [227] demonstrated a millimeter-sized mobile by tightening and loosing the embedded driven tendon. The robot capable of free and robust motion in diverse terrain even three grippers, underneath each body section and inspired by with the existence of obstacles. The robot is involved in the fin ray effect [180], [181], are shaped so that they can simple architecture design in a sheet-like shape, characterized perform a robust grasping of various objects. Gu et al. [205] by silicone-made mechanism where magnetic particles are presented a soft robot prototype that was capable of climbing embedded. Therefore, reference motion and configuration can upright walls. In their study, an EAP membrane was utilized be obtained by regulating the magnetic magnet field. to provide the length-change function. The frictions in the Miyashita et al. [229] designed an origami robot and contacts to the wall can be actively controlled based on demonstrated its walking and swimming performance with electrostatic forces, which is considered as a function of the applied magnetic fields. Made from shape memory polymer applied external voltage. The velocity of the robot depends on (SMP), the presented robot prototype was capable of 1514 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021 thermally self-folding to permit shape adaption when method for congeneric robots with a similar configuration, executing different motion patterns. Liu et al. [230] also e.g., cephalopod-inspired or fish-like morphology in the presented a SMP-made miniature soft robot with four limbs aquatic environment [191], [193], [236], legged system with enabling crawling and jumping locomotion, for the sake of gait-based locomotion strategy [188], [189], cubelike shape medical use. Huang et al. [231] have developed a capable of rolling motion [232], etc., as long as specific magnetically actuated origami-inspired microrobot that mapping of excitations and actuator performance is acquired. permits self-folding, shape reconfiguration and motility, with Indeed, we can refer to modeling methods in a rigid robot to an integrated tail and body morphology that enable better address the common issue, which is to solve the motion swimming efficiency. A mobile soft robot in a cubelike shape equation of the robot system with given forces, torques, thrust, is presented in [232], which can realize rolling motion. In its and other types of actuation. For instance, to model the motion design, each face of the presented robot consisted of four equation of an underwater soft mobile robot given the pneumatically actuated balloons. The locomotion is then propulsion forces generated by a fin-like actuator, researchers generated based on flipping behavior when the balloons at one can also employ the energy-based modeling method [236]. face are expanding. To set free the mobile robot from applied Renda et al. [193] presented a shell-like underwater soft robot, external (magnetic or electric) fields or torques, researchers have contributed to the design work of light-actuated robots in which the Cosserat rod theory was employed to model its [233], [234]. This type of untethered soft mobile robot motion equations. The major difference from rigid robot characterizes sophisticated mobility with periodic light modeling methods is that the variance of internal energy caused by deformation should be considered in the case of soft signals. robot. When mathematically modeling the robot systems that B. Modeling and Control Strategies for Soft Mobile Robot operate underwater or in other interactive environments, Researchers tend to investigate characteristics of the researchers should pay attention to sophisticated actuators utilized in their prototypes and develop the mapping environmental interactions to more accurately explain robot of system inputs and actuator performance. This work can be locomotion. Hence, the integral model of a robot system can observed in previously reviewed publications in this chapter. be obtained by unifying the upfront modeling processes, It can be considered the first step to model the motion considering the underlying principle of the specific actuator equation of the mobile soft robots. Due to a broad selection of adopted, and addressing common issues in modeling robot types of actuators, there is no general modeling method since motion equations in the special working environment. The solutions vary with the working principles of adopted motion of a fish-like mobile robot, propelled by the undulation actuators and the geometry of mechanical structure. For of IPMC-actuated fins, was mathematically modeled [236]. instance, externally applied magnetic fields generate magnetic The proposed model describes how the speed of the robot can forces and torques along a specified direction and thus can be associated with the applied voltage if hydrodynamic effects effectively drive the magnet-actuated soft robot to move in act on the robot system. As for legged robots, whose motion is different terrains and deform it to permit various locomotion dependent on the reaction forces generated at the contact of tasks. Researchers should study how the external field results the robot and the environments, a contact model with specific in material deformability with carefully selected magnetic constraints is necessary to build motion equations and to fields [227] when controlling a magnetically actuated soft guarantee preferred locomotion [187], [198]. In [237], the robot. Electromechanics should be studied in the EAP to authors built the motion equation of the octopus-inspired robot model the strain caused by electrostatic effect. In this process, and analyzed locomotion performance taking into account the researchers should also pay attention to the viscoelasticity of propulsive force at contact as well as the hydrodynamic forces nonlinear dielectric elastomer membrane between two acting on the deformable mechanism. Simple open-loop electrodes. Conventionally, the stress attributed to electrostatic control strategies are commonly adopted in locomotion of a effect, can be modeled into the function of material soft mobile robot, with some exceptions in closed-loop studies permittivity and applied electric field. Thereafter, the to enable accurate motion control in the joint space [238], contraction ratio of the membrane can be computed based on [239] and task space [240]–[242] provided that system the constitutive law of the material [9]. Likewise, dynamic/static models and sensing systems are available. A thermodynamics study is vital for actuators of SMA, SMP, or joint space closed-loop controller was proposed in [238] with other thermally driven materials [235]. We will skip the embedded curvature sensors providing state feedback to detailed modeling method for each of these actuation enable the rolling motion of a circular-shape robot, yet this methods. For more information, interested readers can refer to could hardly guarantee the error convergence in the task previously reviewed publications. The explicit relationship space. Several studies concentrate on the path following of between system excitation and the corresponding robot miniature soft mobile robots actuated by imposed external motion in task space can be obtained by consolidating two (electrical or magnetic) fields [240]–[242]; thus one can models, which, respectively, depict how the actuator performs enable desired locomotion in the task space. A visual servoing with applied excitations and how the robot acts in its task scheme proved viable in path-following tasks [241], where a space with predictable actuator’s performance. Conventional stereo vision system provided real-time 3D position feedback modeling methods can be implemented in modeling robot of a millimeter-scale soft film robot and the proposed motion with solved driving force generated from actuator controller could enable the position error convergence in the

performance. In other words, we can adopt the same modeling task space. XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1515

TABLE IV Soft Mobile Robots

Underwater soft mobile robot On-the-ground soft mobile robot Miniaturized/micronized soft mobile robot Morphology Fish-like Legged robot Legged robot Caterpillar-like Diverse morphologies Depends on working conditions and actuation Swimming motion (e.g., swimming or jumping by shape its body Motion mode through undulatory or Walking motion Walking motion Peristaltic motion and obtain propulsion force [222]; rolling oscillatory motion motion by in sequence pressurize the embed balloons [227], etc.) • For each type of soft mobile robot, modeling work demands specific mapping from the actuation space to the configuration space • Independent analy- • Hydrodynamic effe- sis on actuation pat- • Environmental interaction depending on Modeling cts on robot motion • Hydrodynamic effe- terns of each seg- working conditions • Wave propulsion an- cts on robot motion • Contact model ments and synerge- • Physics at mircoscale if the robot scale is alysis • Contact model tic analysis on inch- down to microscale worm gait Control Closed-loop control can be realized with external sensing device (e.g., 3D visual system, electromagnetic tracking, etc.)

C. Discussion on Soft Mobile Robot control of a soft mobile robot, viable methods are highly Despite the progress in the design and fabrication of soft dependent on the multifactor functioning from their material, mobile robot, there is no report on a general mathematical mechanism and predefined working conditions. modeling method for soft mobile robots as seen in Table IV. V. Conclusion and Discussion The possible reason of this may be attributed to various actuators adopted in robot systems. The mapping between the Soft robotics has shown its continual development in this driven forces applied on the robot and real excitations, e.g., decade. Thus far, the unfaded impetus has driven the field of external field, propulsion forces from body undulation/ robotics into a new era with increased intelligence and oscillation, should be specifically determined. Diverse humanization. On-going research is elevating the level of morphologies (contradictory to a soft continuum robot usually techniques from various disciplines. The range of soft robotics enjoying the same characteristics in the configuration) make it is too broad to be concluded sufficiently here. This paper impossible to construct the mapping of configuration space places emphasis on a very small part of it, as an attempt to and the Cartesian space using an identical modeling method. more intuitively guide interested researchers to quickly learn The motion can be solved with an exactly known driving force about the current progress in the mainstream of soft robot considering the unique structure of mechanism, by adopting prototypes and the way of designing a soft robot system to mathematical modeling methods leveraging equilibrium of implement practically. forces/momentum/energy, or FEM method, etc. Inspired by the morphology of living organisms, soft robots Interestingly, soft mobile robots overlap with soft are more likely to replicate motion patterns and satisfy the continuum robots in a small part, e.g., a legged mobile robot demands of control tasks in various terrains. Their actuated by soft actuators. Merging with deformable soft legs, performance depends on many factors. Evaluating metrics this type of soft robot can better adapt to different terrains and thus should cover aspects of design (flexibility, load capacity, environments by actively shape their configuration, and thus repeatability, response rate, etc.) [243], modeling(fidelity, can provide robust walking performance. The configuration of real-time computing ability, etc.) [89], motion control the individual leg can be depicted by following the same (accuracy, converging rate, robustness, etc.) [244], and method with that of a soft continuum manipulator. However, manipulation (various objects grasping, grasping force, etc.) when modeling the motion of a legged mobile robot, emphasis [245]. Researchers are supposed to solve common issues, should be put on the coordination of multiple legs. Different which include modeling accuracy, interactive ability, real-time working environments faced them also hinder the general controllability, etc. The emphasis should also be placed on modeling methods. Sometimes environmental interactions nontrivial issues attributed to specific characteristics in the should be taken into account if it exerts dominant effects on compliant mechanism. From the perspective of system robot motion. For instance, fluid dynamics should be modeling, these issues cover high nonlinearity of materials, considered when it comes to the underwater working hysteresis in electromechanics and thermodynamics, strong environment; friction and contact model resulting from coupling effects that ubiquitously exist in the nonlinear environmental interaction should be solved in modeling and systems, etc. Though numerous research has been conducted controlling legged soft robots. In summary, the solution of on modeling hysteresis mathematically with known material mapping in between actuation and configuration spaces comes parameters, the tedious and costly offline calibration work for from the analysis of material characteristics under nonlinear elastic materials is required and will complicate external/internal excitations; the mapping between applications of a soft robot if a model-based controller is configuration and task spaces depends on the geometry of the employed. Conventional offline methods sometimes suffer mechanism as well as specific environmental effects. from calibration errors, which degrades modeling accuracy. Therefore, when it comes to the problem of modeling and Control methods for soft robots have been studied these years, 1516 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

e.g., model-based control algorithms [34], [131], model-less [5] P. Polygerinos, N. Correll, S. A. Morin, B. Mosadegh, C. D. Onal, K. Petersen, M. Cianchetti, M. T. Tolley, and R. F. Shepherd, “Soft control based on optimization [129] or online estimation [32], robotics: Review of fluid-driven intrinsically soft devices; and learning-based open-loop control [69], [72]. They do manufacturing, sensing, control, and applications in human-robot exhibit satisfying performance in specific environments but interaction,” Adv. Eng. Mater., vol. 19, no. 12, Article No. 1700016, have their own limits. For instance, researchers usually Dec. 2017.

[6] T. Sénac, A. Lelevé, R. Moreau, C. Novales, L. Nouaille, M. T. Pham, simplify the system modeling by prescribing some and P. Vieyres, “A review of pneumatic actuators used for the design assumptions, e.g., small perturbations to simplify system of medical simulators and medical tools,” Multimodal Technol. nonlinearity, low-speed motion to disentangle coupling of Interact., vol. 3, no. 3, Article No. 47, Jul. 2019. system model, etc. Given real-time requirements, the [7] H. Rodrigue, W. Wang, M. W. Han, T. J. Y. Kim, and S. H. Ahn, “An overview of shape memory alloy-coupled actuators and robots,” Soft complexity of the hyper-redundant system model should be Robot., vol. 4, no. 1, pp. 3–15, Mar. 2017. reduced at the cost of the performance degradation. Limited [8] X. N. Cao, M. Q. Zhang, Z. Zhang, Y. Xu, Y. H. Xiao, and T. F. Li, adaptability of a control algorithm to various environments is “Review of soft linear actuator and the design of a dielectric elastomer another issue that impedes further enhancement in the linear actuator,” Acta Mech. Solida Sin., vol. 32, pp. 566–579, Oct. applicability of soft robots. A possible solution originates 2019.

[9] G. Y. Gu, J. Zhu, L. M. Zhu, and X. Y. Zhu, “A survey on dielectric from the development of robust control algorithms combined elastomer actuators for soft robots,” Bioinspir. Biomim., vol. 12, with more advanced sensing methods that improve the ability Article No. 011003, Jan. 2017.

of environmental cognition. Actuators based on smart [10] S. G. Fitzgerald, G. W. Delaney, and D. Howard, “A review of materials sometimes show delays in actuation. Therefore, jamming actuation in soft robotics,” Actuators, vol. 9, no. 4, Article No. 104, Oct. 2020. further study on advanced materials is also required to

[11] L. Hines, K. Petersen, G. Z. Lum, and M. Sitti, “Soft actuators for improve the performance of actuators. small-scale robotics,” Adv. Mater., vol. 29, no. 13, Article No. Soft robotics is considered to be a highly interdisciplinary 1603483, Apr. 2017.

subject; breakthroughs thus require closer multi-discipline [12] T. G. Thuruthel, Y. Ansari, E. Falotico, and C. Laschi, “Control collaboration. Most existing publications have studied the strategies for soft robotic manipulators: A survey,” Soft Robot., vol. 5, pp. 149–163, Apr. 2018. design and fabrication of soft robot prototypes from bio-

[13] C. Y. Chu and R. M. Patterson, “Soft robotic devices for hand inspired approaches. Due to the internal relationship between rehabilitation and assistance: A narrative review,” J. Neuroeng. the morphology and sensorimotor control, the presented Rehabil., vol. 15, no. 1, Article No. 9, Feb. 2018.

robots have the potentials to perform similar motions to those [14] M. Cianchetti, C. Laschi, A. Menciassi, and P. Dario, “Biomedical of living organisms. By gaining insights into the underlying applications of soft robotics,” Nat. Rev. Mater., vol. 3, pp. 143–153, Jun. 2018. principle of morphology, locomotion, and sensorimotor

[15] M. W. Gifari, H. Naghibi, S. Stramigioli, and M. Abayazid, “A review control, the replicated motion patterns are more likely to be on recent advances in soft surgical robots for endoscopic applications,” achieved on soft robot platforms. They can then demonstrate Int. J. Med. Robot., vol. 15, no. 5, Article No. e2010, Oct. 2019.

intelligence, agility, robustness on par with those of their [16] W. S. Chu, K. T. Lee, S. H. Song, M. W. Han, J. Y. Lee, H. S. Kim, biology counterparts. More functional materials lay the basis M. S. Kim, Y. J. Park, K. J. Cho, and S. H. Ahn, “Review of biomimetic underwater robots using smart actuators,” Int. J. Precis. for the development of soft robot prototypes. Optimized Eng. Manuf., vol. 13, pp. 1281–1292, Jul. 2012. mechanical design helps to better learn bio-inspired motion [17] A. Raj and A. Thakur, “Fish-inspired robots: design, sensing, strategies. Thereafter, having a control methodology enhances actuation, and autonomy—a review of research,” Bioinspir. Biomim., their performance in accuracy and versatility, with computer vol. 11, no. 3, Article No. 031001, Apr. 2016. technology jointly contributing to improving the capabilities [18] R. Pfeifer, M. Lungarella, and F. Iida, “Self-organization, embodiment, and biologically inspired robotics,” Science, vol. 318, no. 5853, of real-time planning, sensing, recognizing and acting. pp. 1088–1093, Nov. 2007. This paper presents a review work on the scientific studies [19] E. J. Markvicka, M. D. Bartlett, X. N. Huang, and C. Majidi, “An of soft robotics, in the framework of commonly adopted autonomously electrically self-healing liquid metal-elastomer morphologies and corresponding motion strategies, aiming to composite for robust soft-matter robotics and electronics,” Nat. Mater., vol. 17, pp. 618–624, Jul. 2018. help new researchers easily step into this domain.

[20] Q. Shen, S. Trabia, T. Stalbaum, V. Palmre, K. Kim, and I. K. Oh, “A Nevertheless, there is still a long way ahead for prospective multiple-shape memory polymer-metal composite actuator capable of applications. This can be achieved with more efforts and more programmable control, creating complex 3D motion of bending, cooperation devoted by researchers from diverse backgrounds. twisting, and oscillation,” Sci. Rep., vol. 6, Article No. 24462, Apr. 2016.

[21] M. Wehner, R. L. Truby, D. J. Fitzgerald, B. Mosadegh, G. M. References Whitesides, J. A. Lewis, and R. J. Wood, “An integrated design and fabrication strategy for entirely soft, autonomous robots,” Nature, [1] C. Majidi, “Soft robotics: A perspective—current trends and prospects vol. 536, no. 7617, pp. 451–455, Aug. 2016. for the future,” Soft Robot., vol. 1, no. 1, pp. 5–11, Mar. 2014.

[22] L. Migliorini, T. Santaniello, Y. S. Yan, C. Lenardi, and P. Milani, [2] C. Laschi, B. Mazzolai, and M. Cianchetti, “Soft robotics: “Low-voltage electrically driven homeostatic hydrogel-based actuators Technologies and systems pushing the boundaries of robot abilities,” for underwater soft robotics,” Sens. Actuators B: Chem., vol. 228, Sci. Robot., vol. 1, no. 1, Article No. eaah3690, Dec. 2016. pp. 758–766, Jun. 2016.

[3] D. Rus and M. T. Tolley, “Design, fabrication and control of soft [23] Y. Yekutieli, R. Sagiv-Zohar, R. Aharonov, Y. Engel, B. Hochner, and robots,” Nature, vol. 521, no. 7553, pp. 467–475, May 2015. T. Flash, “Dynamic model of the octopus arm. I. Biomechanics of the

[4] J. Z. Gul, M. Sajid, M. M. Rehman, G. U. Siddiqui, I. Shah, K. H. octopus reaching movement,” J. Neurophysiol., vol. 94, no. 2, Kim, J. W. Lee, and K. H. Choi, “3D printing for soft robotics-a pp. 1443–1458, Aug. 2005. review,” Sci. Technol. Adv. Mater., vol. 19, no. 1, pp. 243–262, Mar. [24] W. M. Kier and K. K. Smith, “Tongues, tentacles and trunks: The 2018. biomechanics of movement in muscular-hydrostats,” Zool. J. Linn. XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1517

Soc., vol. 83, no. 4, pp. 307–324, Apr. 1985. Access, vol. 7, pp. 57151–57162, May 2019.

[25] H. Shigemune, V. Cacucciolo, M. Cianchetti, H. Sawada, S. [44] M. M. Tonapi, I. S. Godage, A. M. Vijaykumar, and I. D. Walker, Hashimoto, and C. Laschi, “Effect of base rotation on the “Spatial kinematic modeling of a long and thin continuum robotic controllability of a redundant soft robotic arm,” in Proc. IEEE Int. cable,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA), Seattle, Conf. Soft Robotics (RoboSoft), Livorno, Italy, 2018, pp. 350–355. WA, USA, 2015, pp. 3755–3761.

[26] C. Laschi, M. Cianchetti, B. Mazzolai, L. Margheri, M. Follador, and [45] M. M. Tonapi, I. S. Godage, and I. D. Walker, “Design, modeling and P. Dario, “Soft robot arm inspired by the octopus,” Adv. Robot., performance evaluation of a long and slim continuum robotic cable,” vol. 26, no. 7, pp. 709–727, Apr. 2012. in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Chicago, IL, USA, 2014, pp. 2852–2859. [27] F. Renda, M. Giorelli, M. Calisti, M. Cianchetti, and C. Laschi,

“Dynamic model of a multibending soft robot arm driven by cables,” [46] R. K. Katzschmann, A. D. Marchese, and D. Rus, “Autonomous object IEEE Trans. Robotics, vol. 30, no. 5, pp. 1109–1122, Oct. 2014. manipulation using a soft planar grasping manipulator,” Soft Robot., vol. 2, no. 4, pp. 155–164, Dec. 2015. [28] F. Maghooa, A. Stilli, Y. Noh, K. Althoefer, and H. A. Wurdemann,

“Tendon and pressure actuation for a bio-inspired manipulator based [47] R. K. Katzschmann, C. Della Santina, Y. Toshimitsu, A. Bicchi, and on an antagonistic principle,” in Proc. IEEE Int. Conf. Robotics and D. Rus, “Dynamic motion control of multi-segment soft robots using Autom. (ICRA), Seattle, WA, USA, 2015, pp. 2556–2561. piecewise constant curvature matched with an augmented rigid body model,” in Proc. 2nd IEEE Int. Conf. Soft Robotics (RoboSoft), Seoul, [29] D. Trivedi, A. Lotfi, and C. D. Rahn, “Geometrically exact models for soft robotic manipulators,” IEEE Trans. Robot., vol. 24, no. 4, Korea (South), 2019, pp. 454–461.

pp. 773–780, Aug. 2008. [48] A. D. Marchese and D. Rus, “Design, kinematics, and control of a soft spatial fluidic elastomer manipulator,” The Int. J. Robotics Research, [30] Z. X. Xie, F. Y. Yuan, Z. M. Liu, Z. N. Sun, E. M. Knubben, and L. Wen, “A proprioceptive soft tentacle gripper based on crosswise vol. 35, no. 7, pp. 840–869, Jun. 2016.

stretchable sensors,” IEEE/ASME Trans. Mechatron., vol. 25, no. 4, [49] R. V. Martinez, J. L. Branch, C. R. Fish, L. H. Jin, R. F. Shepherd, R. pp. 1841–1850, Aug. 2020. M. D. Nunes, Z. G. Suo, and G. M. Whitesides, “Robotic tentacles with three-dimensional mobility based on flexible elastomers,” Adv. [31] M. D. Grissom, V. Chitrakaran, D. Dienno, M. Csencits, M. Pritts, B. Jones, W. McMahan, D. Dawson, C. Rahn, and I. Walker, “Design and Mater., vol. 25, no. 2, pp. 205–212, Jan. 2013.

experimental testing of the octarm soft robot manipulator,” in Proc. [50] H. S. Wang, C. Wang, W. D. Chen, X. W. Liang, and Y. T. Liu, SPIE 6230, Unmanned Systems Technology VIII, Florida, United “Three-dimensional dynamics for cable-driven soft manipulator,” States, 2006. IEEE/ASME Trans. Mechatron., vol. 22, no. 1, pp. 18–28, Feb. 2017.

[32] M. H. Li, R. J. Kang, D. T. Branson, and J. S. Dai, “Model-free control [51] T. G. Thuruthel, E. Falotico, F. Renda, and C. Laschi, “Model-based for continuum robots based on an adaptive kalman filter,” IEEE/ASME reinforcement learning for closed-loop dynamic control of soft robotic Trans. Mechatron., vol. 23, no. 1, pp. 286–297, Feb. 2018. manipulators,” IEEE Trans. Robot., vol. 35, no. 1, pp. 124–134, Feb.

[33] V. Falkenhahn, T. Mahl, A. Hildebrandt, R. Neumann, and O. 2019.

Sawodny, “Dynamic modeling of bellows-actuated continuum robots [52] D. C. Rucker, B. A. Jones, and I. R. J. Webster III, “A geometrically using the Euler-Lagrange formalism,” IEEE Trans. Robot., vol. 31, exact model for externally loaded concentric-tube continuum robots,” no. 6, pp. 1483–1496, Dec. 2015. IEEE Trans. Robot., vol. 26, no. 5, pp. 769–780, Oct. 2010.

[34] V. Falkenhahn, A. Hildebrandt, R. Neumann, and O. Sawodny, [53] J. Linn, H. Lang, and A. Tuganov, “Geometrically exact Cosserat rods “Dynamic control of the bionic handling assistant,” IEEE/ASME with Kelvin-Voigt type viscous damping,” Mech. Sci., vol. 4, Trans. Mechatron., vol. 22, no. 1, pp. 6–17, Feb. 2017. pp. 79–96, Feb. 2013.

[35] M. Rolf and J. J. Steil, “Constant curvature continuum kinematics as [54] A. D. Marchese, R. Tedrake, and D. Rus, “Dynamics and trajectory fast approximate model for the Bionic Handling Assistant,” in Proc. optimization for a soft spatial fluidic elastomer manipulator,” Int. J. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Vilamoura- Robot. Res., vol. 35, no. 8, pp. 1000–1019, Jul. 2016. Algarve, Portugal, 2012, pp. 3440–3446.

[55] F. Renda, M. Cianchetti, M. Giorelli, A. Arienti, and C. Laschi, “A 3D

[36] T. Mahl, A. Hildebrandt, and O. Sawodny, “A variable curvature steady-state model of a tendon-driven continuum soft manipulator continuum kinematics for kinematic control of the bionic handling inspired by the octopus arm,” Bioinspir. Biomim., vol. 7, no. 2, Article assistant,” IEEE Trans. Robot., vol. 30, no. 4, pp. 935–949, Aug. 2014. No. 025006, Jun. 2012.

[37] T. Mahl, A. E. Mayer, A. Hildebrandt, and O. Sawodny, “A variable [56] H. S. Wang, W. D. Chen, X. J. Yu, T. Deng, X. Z. Wang, and R. curvature modeling approach for kinematic control of continuum Pfeifer, “Visual servo control of cable-driven soft robotic manipulators,” in Proc. American Control Conf., Washington, DC, manipulator,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and USA, 2013, pp. 4945–4950. Systems, Tokyo, Japan, 2013, pp. 57–62.

[38] V. Falkenhahn, F. A. Bender, A. Hildebrandt, R. Neumann, and O. [57] H. S. Wang, R. X. Zhang, W. D. Chen, X. Z. Wang, and R. Pfeifer, “A Sawodny, “Online TCP trajectory planning for redundant continuum cable-driven soft robot surgical system for cardiothoracic endoscopic manipulators using quadratic programming,” in Proc. IEEE Int. Conf. surgery: Preclinical tests in animals,” Surg. Endosc., vol. 31, Advanced Intelligent Mechatronics (AIM), Banff, AB, Canada, 2016, pp. 3152–3158, Aug. 2017. pp. 1163–1168.

[58] R. L. Truby, C. D. Santina, and D. Rus, “Distributed proprioception of

[39] L. Toscano, V. Falkenhahn, A. Hildebrandt, F. Braghin, and O. 3D configuration in soft, sensorized robots via deep learning,” IEEE Sawodny, “Configuration space impedance control for continuum Robot. Autom. Lett., vol. 5, no. 2, pp. 3299–3306, Apr. 2020. manipulators,” in Proc. 6th Int. Conf. Autom., Robotics and Applications (ICARA), Queenstown, New Zealand, 2015, pp. 597–602. [59] R. J. Kang, Y. Guo, L. S. Chen, D. T. Branson, and J. S. Dai, “Design of a pneumatic muscle based continuum robot with embedded

[40] A. D. Marchese, K. Komorowski, C. D. Onal, and D. Rus, “Design tendons,” IEEE/ASME Trans. Mechatron., vol. 22, no. 2, pp. 751–761, and control of a soft and continuously deformable 2D robotic Apr. 2017. manipulation system,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA), Hong Kong, China, 2014, pp. 2189–2196. [60] A. Firouzeh, M. Salerno, and J. Paik, “Stiffness control with shape memory polymer in underactuated robotic origamis,” IEEE Trans.

[41] A. D. Marchese, R. K. Katzschmann, and D. Rus, “Whole arm Robot., vol. 33, no. 4, pp. 765–777, Aug. 2017. planning for a soft and highly compliant 2D robotic manipulator,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Chicago, [61] R. J. Webster III and B. A. Jones, “Design and kinematic modeling of IL, USA, 2014, pp. 554–560. constant curvature continuum robots: A review,” Int. J. Robot. Res., vol. 29, no. 13, pp. 1661–1683, Nov. 2010.

[42] R. Mutlu, G. Alici, X. C. Xiang, and W. H. Li, “Electro-mechanical modelling and identification of electroactive polymer actuators as [62] B. A. Jones and I. D. Walker, “Kinematics for multisection continuum smart robotic manipulators,” Mechatronics, vol. 24, no. 3, pp. 241–251, robots,” IEEE Trans. Robot., vol. 22, no. 1, pp. 43–55, Feb. 2006.

Apr. 2014. [63] H. El-Hussieny, S. G. Jeong, and J. H. Ryu, “Dynamic modeling of a class of soft growing robots using euler-lagrange formalism,” in Proc. [43] L. Li, T. Jin, Y. Z. Tian, F. Yang, and F. F. Xi, “Design and analysis of a square-shaped continuum robot with better grasping ability,” IEEE SICE Annu. Conf., Hiroshima, Japan, 2019, pp. 453–458. 1518 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

[64] T. G. Thuruthel, E. Falotico, M. Cianchetti, and C. Laschi, “Learning problems,” Int. J. Impact Eng., vol. 36, no. 5, pp. 659–666, May 2009. global inverse kinematics solutions for a continuum robot,” in Proc. [84] W. S. Rone and P. Ben-Tzvi, “Continuum robot dynamics utilizing the Symp. Robot Design, Dynamics and Control, Udine, Italy, 2016, pp. principle of virtual power,” IEEE Trans. Robot., vol. 30, no. 1, 47–54. pp. 275–287, Feb. 2014.

[65] G. S. Chirikjian and J. W. Burdick, “A modal approach to hyper- [85] F. Xu, H. S. Wang, J. C. Wang, K. W. S. Au, and W. D. Chen, redundant manipulator kinematics,” IEEE Trans. Robot. Autom., “Underwater dynamic visual servoing for a soft robot arm with online vol. 10, no. 3, pp. 343–354, Jun. 1994. distortion correction,” IEEE/ASME Trans. Mechatron., vol. 24, no. 3,

[66] K. M. Digumarti, B. Trimmer, A. T. Conn, and J. Rossiter, pp. 979–989, Jun. 2019. “Quantifying dynamic shapes in soft morphologies,” Soft Robot.,

[86] P. Jung, S. Leyendecker, J. Linn, and M. Ortiz, “Discrete Lagrangian vol. 6, no. 6, pp. 733–744, Dec. 2019. mechanics and geometrically exact Cosserat rods,” in Proc. Multibody

[67] T. Li, K. Nakajima, and R. Pfeifer, “Online learning for behavior Dynamics, ECCOMAS Thematic Conf., Warsaw, Poland, 2009. switching in a soft robotic arm,” in Proc. IEEE Int. Conf. Robotics and

[87] S. S. Antman, Nonlinear Problems of Elasticity. New York: Springer- Autom., Karlsruhe, Germany, 2013, pp. 1296–1302. Verlag, 1995.

[68] T. Li, K. Nakajima, M. Cianchetti, C. Laschi, and R. Pfeifer,

[88] D. C. Rucker and R. J. Webster, “Computing Jacobians and “Behavior switching using reservoir computing for a soft robotic arm,” compliance matrices for externally loaded continuum robots,” in Proc. in Proc. IEEE Int. Conf. Robotics and Autom., Saint Paul, MN, USA, IEEE Int. Conf. Robotics and Autom., Shanghai, China, 2011, pp. 2012, pp. 4918–4924. 945–950.

[69] M. Rolf and J. J. Steil, “Efficient exploratory learning of inverse

[89] J. Till, V. Aloi, and C. Rucker, “Real-time dynamics of soft and kinematics on a bionic elephant trunk,” IEEE Trans. Neural Networks continuum robots based on Cosserat rod models,” Int. J. Robot. Res., and Learning Systems, vol. 25, no. 6, pp. 1147–1160, Jun. 2014. vol. 38, no. 6, pp. 723–746, May 2019.

[70] M. Giorelli, F. Renda, M. Calisti, A. Arienti, G. Ferri, and C. Laschi,

[90] Z. K. Zhang, J. Dequidt, A. Kruszewski, F. Largilliere, and C. Duriez, “Learning the inverse kinetics of an octopus-like manipulator in three- “Kinematic modeling and observer based control of soft robot using dimensional space,” Bioinspir. Biomim., vol. 10, Article No. 035006, real-time finite element method,” in Proc. IEEE/RSJ Int. Conf. May 2015. Intelligent Robots and Systems (IROS), Daejeon, Korea (South), 2016,

[71] T. G. Thuruthel, E. Falotico, M. Cianchetti, F. Renda, and C. Laschi, pp. 5509–5514. “Learning global inverse statics solution for a redundant soft robot,” in Proc. 13th Int. Conf. Informatics in Control, Autom. and Robotics, [91] E. Coevoet, A. Escande, and C. Duriez, “Optimization-based inverse Lisbon, Portugal, 2016, pp. 303–310. model of soft robots with contact handling,” IEEE Robot. Autom. Lett., vol. 2, no. 3, pp. 1413–1419, Jul. 2017.

[72] M. Giorelli, F. Renda, M. Calisti, A. Arienti, G. Ferri, and C. Laschi, “Neural network and jacobian method for solving the inverse statics of [92] Z. K. Zhang, T. M. Bieze, J. Dequidt, A. Kruszewski, and C. Duriez, a cable-driven soft arm with nonconstant curvature,” IEEE Trans. "Visual servoing control of soft robots based on finite element model,” Robot., vol. 31, no. 4, pp. 823–834, Aug. 2015. in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS), Vancouver, BC, Canada, 2017, pp. 2895–2901.

[73] M. Giorelli, F. Renda, G. Ferri, and C. Laschi, “A feed-forward neural network learning the inverse kinetics of a soft cable-driven [93] S. Grazioso, G. Di Gironimo, and B. Siciliano, “A geometrically exact manipulator moving in three-dimensional space,” in Proc. IEEE/RSJ model for soft continuum robots: The finite element deformation space Int. Conf. Intelligent Robots and Systems, Tokyo, Japan, 2013, pp. formulation,” Soft Robotics, vol. 6, no. 6, pp. 790–811, Dec. 2019.

5033–5039. [94] S. D. Barforooshi and A. K. Mohammadi, “Study neo-Hookean and Yeoh hyper-elastic models in dielectric elastomer-based micro-beam [74] M. Dehghani and S. A. A. Moosavian, “Dynamics modeling of planar continuum robots by finite circular elements for motion control,” in resonators,” Lat. Am. J. Solids Struct., vol. 13, no. 10, pp. 1823–1837, Proc. AI & Robotics (IRANOPEN), Qazvin, Iran, 2015, pp. 1–6. Oct. 2016.

[95] S. Kut, G. Ryzinska, and B. Niedzialek, “Numerical analysis and [75] M. Dehghani and S. A. A. Moosavian, “Statics modeling of planar continuum robots using virtual energy method,” in Proc. 2nd RSI/ISM experimental verification of elastomer bending process with different Int. Conf. Robotics and Mechatronics (ICRoM), Tehran, Iran, 2014, material models,” Open Eng., vol. 6, no. 1, pp. 228–234, Jun. 2016.

pp. 474–479. [96] R. S. Penning, J. Jung, J. A. Borgstadt, N. J. Ferrier, and M. R. Zinn, “Towards closed loop control of a continuum robotic manipulator for [76] J. Lock, G. Laing, M. Mahvash, and P. E. Dupont, “Quasistatic modeling of concentric tube robots with external loads,” in Proc. medical applications,” in Proc. IEEE Int. Conf. Robotics and Autom., IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Taipei, China, Shanghai, China, 2011, pp. 4822–4827.

2010, pp. 2325–2332. [97] J. Jung, R. S. Penning, N. J. Ferrier, and M. R. Zinn, “A modeling approach for continuum robotic manipulators: Effects of nonlinear [77] F. Renda and C. Laschi, “A general mechanical model for tendon- driven continuum manipulators,” in Proc. IEEE Int. Conf. Robotics internal device friction,” in Proc. IEEE/RSJ Int. Conf. Intelligent and Autom., St Paul, MN, USA, 2012, pp. 3813–3818. Robots and Systems, San Francisco, CA, USA, 2011, pp. 5139–5146.

[78] D. C. Rucker and R. J. Webster III, “Statics and dynamics of [98] G. Subramani and M. R. Zinn, “Tackling friction-an analytical continuum robots with general tendon routing and external loading,” modeling approach to understanding friction in single tendon driven IEEE Trans. Robot., vol. 27, no. 6, pp. 1033–1044, Dec. 2011. continuum manipulators,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA), Seattle, WA, USA, 2015, pp. 610–617.

[79] F. Renda, V. Cacucciolo, J. Dias, and L. Seneviratne, “Discrete

Cosserat approach for soft robot dynamics: A new piece-wise constant [99] R. Roy, L. Wang, and N. Simaan, “Modeling and estimation of strain model with torsion and shears,” in Proc. IEEE/RSJ Int. Conf. friction, extension, and coupling effects in multisegment continuum Intelligent Robots and Systems (IROS), Daejeon, Korea (South), 2016, robots,” IEEE/ASME Trans. Mechatron., vol. 22, no. 2, pp. 909–920, pp. 5495–5502. Apr. 2017.

[80] F. Xu, H. S. Wang, K. W. S. Au, W. D. Chen, and Y. Z. Miao, [100] D. B. Camarillo, C. F. Milne, C. R. Carlson, M. R. Zinn, and J. K. “Underwater dynamic modeling for a cable-driven soft robot arm,” Salisbury, “Mechanics modeling of tendon-driven continuum IEEE/ASME Trans. Mechatron., vol. 23, no. 6, pp. 2726–2738, Dec. manipulators,” IEEE Trans. Robot., vol. 24, no. 6, pp. 1262–1273, Dec. 2018. 2008.

[81] I. Tunay, “Spatial continuum models of rods undergoing large [101] D. B. Camarillo, C. R. Carlson, and J. K. Salisbury, “Configuration deformation and inflation,” IEEE Trans. Robot., vol. 29, no. 2, tracking for continuum manipulators with coupled tendon drive,” IEEE pp. 297–307, Apr. 2013. Trans. Robot., vol. 25, no. 4, pp. 798–808, Aug. 2009.

[82] E. Tatlicioglu, I. D. Walker, and D. M. Dawson, “Dynamic modelling [102] I. D. Mayergoyz and G. Friedman, “Generalized preisach model of for planar extensible continuum robot manipulators,” in Proc. IEEE hysteresis,” IEEE Trans. Magn., vol. 24, no. 1, pp. 212–217, Jan. 1988. Int. Conf. Robotics and Autom., Rome, Italy, 2007, pp. 1357–1362. [103] M. Al Janaideh, S. Rakheja, and C. Y. Su, “An analytical generalized

[83] C. Renaud, J. M. Cros, Z. Q. Feng, and B. T. Yang, “The Yeoh model Prandtl-Ishlinskii model inversion for hysteresis compensation in applied to the modeling of large deformation contact/impact micropositioning control,” IEEE/ASME Trans. Mechatron., vol. 16, XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1519

no. 4, pp. 734–744, Aug. 2011. [124] R. E. Goldman, A. Bajo, and N. Simaan, “Compliant motion control for multisegment continuum robots with actuation force sensing,” [104] P. Chen, X. X. Bai, L. J. Qian, and S. B. Choi, “An approach for hysteresis modeling based on shape function and memory IEEE Trans. Robot., vol. 30, no. 4, pp. 890–902, Aug. 2014.

mechanism,” IEEE/ASME Trans. Mechatron., vol. 23, no. 3, pp. 1270– [125] A. Bajo and N. Simaan, “Hybrid motion/force control of multi- 1278, Jun. 2018. backbone continuum robots,” Int. J. Robot. Res., vol. 35, no. 4, pp. 422–434, Apr. 2016. [105] V. K. Chitrakaran, A. Behal, D. M. Dawson, and I. D. Walker,

“Setpoint regulation of continuum robots using a fixed camera,” [126] A. Bajo, R. B. Pickens, S. D. Herrell, and N. Simaan, “Constrained Robotica, vol. 25, no. 5, pp. 581–586, Sep. 2007. motion control of multisegment continuum robots for transurethral bladder resection and surveillance,” in Proc. IEEE Int, Conf, Robotics [106] H. S. Wang, R. X. Zhang, W. D. Chen, X. W. Liang, and R. Pfeifer, “Shape detection algorithm for soft manipulator based on fiber bragg and Autom., Karlsruhe, Germany, 2013, pp. 5837–5842.

gratings,” IEEE/ASME Trans. Mechatron., vol. 21, no. 6, pp. 2977– [127] L. Wu, K. Y. Wu, and H. L. Ren, “Towards hybrid control of a flexible 2982, Dec. 2016. curvilinear surgical robot with visual/haptic guidance,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS), Daejeon,

[107] X. Ma, P. W. Y. Chiu, and Z. Li, “Real-time deformation sensing for flexible manipulators with bending and twisting,” IEEE Sens. J., Korea (South), 2016, pp. 501–507.

vol. 18, no. 15, pp. 6412–6422, Aug. 2018. [128] G. Smoljkic, G. Borghesan, D. Reynaerts, J. De Schutter, J. V. Sloten, and E. V. Poorten, “Constraint-based interaction control of robots

[108] W. Felt, K. Y. Chin, and C. D. Remy, “Contraction sensing with smart braid McKibben muscles,” IEEE/ASME Trans. Mechatron., vol. 21, featuring large compliance and deformation,” IEEE Trans. Robot., no. 3, pp. 1201–1209, Jun. 2016. vol. 31, no. 5, pp. 1252–1260, Oct. 2015.

[129] M. C. Yip and D. B. Camarillo, “Model-less feedback control of

[109] G. Gerboni, A. Diodato, G. Ciuti, M. Cianchetti, and A. Menciassi, “Feedback control of soft robot actuators via commercial flex bend continuum manipulators in constrained environments,” IEEE Trans. sensors,” IEEE/ASME Trans. Mechatron., vol. 22, no. 4, pp. 1881– Robot., vol. 30, no. 4, pp. 880–889, Aug. 2014.

1888, Aug. 2017. [130] M. C. Yip and D. B. Camarillo, “Model-less hybrid position/force control: A minimalist approach for continuum manipulators in

[110] R. Xu, A. Yurkewich, and R. V. Patel, “Curvature, torsion, and force sensing in continuum robots using helically wrapped FBG sensors,” unknown, constrained environments,” IEEE Robot. Autom. Lett., vol. 1, no. 2, pp. 844–851, Jul. 2016. IEEE Robot. Autom. Lett., vol. 1, no. 2, pp. 1052–1059, Jul. 2016.

[131] C. Della Santina, R. K. Katzschmann, A. Biechi, and D. Rus,

[111] Y. Bailly, Y. Amirat, and G. Fried, “Modeling and control of a “Dynamic control of soft robots interacting with the environment,” in continuum style microrobot for endovascular surgery,” IEEE Trans. Proc. IEEE Int. Conf. Soft Robotics (RoboSoft), Livorno, Italy, 2018, Robot., vol. 27, no. 5, pp. 1024–1030, Oct. 2011. pp. 46–53.

[112] A. V. Kudryavtsev, M. T. Chikhaoui, A. Liadov, P. Rougeot, F.

[132] H. S. Wang, H. Ni, J. C. Wang, and W. D. Chen, “Hybrid vision/force Spindler, K. Rabenorosoa, J. Burgner-Kahrs, B. Tamadazte, and N. control of soft robot based on a deformation model,” IEEE Trans. Andreff, “Eye-in-hand visual servoing of concentric tube robots,” Control Systems Technology, vol. 29, no. 2, pp. 661–671, Mar. 2021. IEEE Robot. Autom. Lett., vol. 3, no. 3, pp. 2315–2321, Jul. 2018.

[133] B. Deutschmann, M. Chalon, J. Reinecke, M. Maier, and C. Ott, “Six-

[113] J. Z. Gul, K. Y. Su, and K. H. Choi, “Fully 3D printed multi-material DoF pose estimation for a tendon-driven continuum mechanism soft bio-inspired whisker sensor for underwater-induced vortex without a deformation model,” IEEE Robot. Autom. Lett., vol. 4, no. 4, detection,” Soft Robot., vol. 5, no. 2, pp. 122–132, Apr. 2018. pp. 3425–3432, Oct. 2019.

[114] M. Neumann and J. Burgner-Kahrs, “Considerations for follow-the-

[134] A. Ataka, A. Shiva, H. K. Lam, and K. Althoefer, “Magnetic-field- leader motion of extensible tendon-driven continuum robots,” in Proc. inspired Navigation for Soft Continuum Manipulator,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA), Stockholm, Sweden, IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Madrid, Spain, 2016, pp. 917–923. 2018, pp. 168–173.

[115] D. Palmer, S. Cobos-Guzman, and D. Axinte, “Real-time method for

[135] I. S. Godage, D. T. Branson, E. Guglielmino, and D. G. Caldwell, tip following navigation of continuum snake arm robots,” Robot. “Path planning for multisection continuum arms,” in Proc. IEEE Int. Autonom. Syst., vol. 62, no. 10, pp. 1478–1485, Oct. 2014. Conf. Mechatronics and Autom., Chengdu, China, 2012, pp.

[116] H. B. Gilbert, J. Neimat, and R. J. Webster, “Concentric tube robots as 1208–1213. steerable needles: Achieving follow-the-leader deployment,” IEEE

[136] P. L. Anderson, A. W. Mahoney, and R. J. Webster, “Continuum Trans. Robot., vol. 31, no. 2, pp. 246–258, Apr. 2015. reconfigurable parallel robots for surgery: Shape sensing and state

[117] B. Ouyang, Y. H. Liu, and D. Sun, “Design and shape control of a estimation with uncertainty,” IEEE Robot. Autom. Lett., vol. 2, no. 3, three-section continuum robot,” in Proc. IEEE Int. Conf. Advanced pp. 1617–1624, Jul. 2017. Intelligent Mechatronics (AIM), Banff, Canada, 2016, pp. 1151–1156.

[137] D. Trivedi and C. D. Rahn, “Model-based shape estimation for soft

[118] L. Dupourqué, F. Masaki, Y. L. Colson, T. Kato, and N. Hata, robotic manipulators: The planar case,” J. Mech. Robot., vol. 6, no. 2, “Transbronchial biopsy catheter enhanced by a multisection continuum Article No. 021005, May 2014. robot with follow-the-leader motion,” Int. J. Comput. Assist. Radiol.

[138] V. K. Venkiteswaran, J. Sikorski, and S. Misra, “Shape and contact Surg., vol. 14, no. 11, pp. 2021–2029, Nov. 2019. force estimation of continuum manipulators using pseudo rigid body

[119] G. Fang, X. M. Wang, K. Wang, K. H. Lee, J. D. L. Ho, H. C. Fu, D. models,” Mech. Mach. Theory, vol. 139, pp. 34–45, Sep. 2019. K. C. Fu, and K. W. Kwok, “Vision-based online learning kinematic

[139] M. Khoshnam and R. V. Patel, “Estimating contact force for steerable control for soft robots using local Gaussian process regression,” IEEE ablation catheters based on shape analysis,” in Proc. IEEE/RSJ Int. Robot. Autom. Lett., vol. 4, no. 2, pp. 1194–1201, 2019. Conf. Intelligent Robots and Systems, Chicago, IL, USA, 2014, pp.

[120] H. S. Wang, B. H. Yang, Y. T. Liu, W. D. Chen, X. W. Liang, and R. 3509–3514. Pfeifer, “Visual servoing of soft robot manipulator in constrained

[140] D. C. Rucker and R. J. Webster, “Deflection-based force sensing for environments with an adaptive controller,” IEEE/ASME Trans. continuum robots: A probabilistic approach,” in Proc. IEEE/RSJ Int. Mechatron., vol. 22, no. 1, pp. 41–50, Feb. 2017. Conf. Intelligent Robots and Systems, San Francisco, CA, USA, 2011,

[121] F. Xu, H. S. Wang, W. D. Chen, and Y. Z. Miao, “Visual servoing of a pp. 3764–3769. cable-driven soft robot manipulator with shape feature,” IEEE Robot. [141] K. Xu and N. Simaan, “An investigation of the intrinsic force sensing Autom. Lett, vol. 6, no. 3, pp. 4281–4288, 2021. capabilities of continuum robots,” IEEE Trans. Robot., vol. 24, no. 3,

[122] M. Mahvash and P. E. Dupont, “Stiffness control of surgical pp. 576–587, Jun. 2008. continuum manipulators,” IEEE Trans. Robot., vol. 27, no. 2, pp. 334– [142] R. Roy, L. Wang, and N. Simaan, “Investigation of effects of 345, Apr. 2011. dynamics on intrinsic wrench sensing in continuum robots,” in Proc.

[123] R. E. Goldman, A. Bajo, and N. Simaan, “Compliant motion control IEEE Int. Conf. Robotics and Autom. (ICRA), Stockholm, Sweden, for continuum robots with intrinsic actuation sensing,” in Proc. IEEE 2016, pp. 2052–2059. Int. Conf. Robotics and Autom., Shanghai, China, 2011, pp. [143] F. Khan, R. J. Roesthuis, and S. Misra, “Force sensing in continuum 1126–1132. manipulators using fiber bragg grating sensors,” in Proc. IEEE/RSJ 1520 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

Int. Conf. Intelligent Robots and Systems (IROS), Vancouver, BC, Whitesides, “Soft robotics for chemists,” Angew. Chem., Int. Ed., Canada, 2017, pp. 2531–2536. vol. 50, no. 8, pp. 1890–1895, Feb. 2011.

[144] S. Hasanzadeh and F. Janabi-Sharifi, “Model-based force estimation [164] M. Controzzi, C. Cipriani, and M. C. Carrozza, “Design of artificial for intracardiac catheters,” IEEE/ASME Trans. Mechatron., vol. 21, hands: A review,” in the Human Hand as an Inspiration for Robot no. 1, pp. 154–162, Feb. 2016. Hand Development, R. Balasubramanian and V. Santos, Eds. Switzerland: Springer, 2014, pp. 219–246. [145] J. Back, L. Lindenroth, R. Karim, K. Althoefer, K. Rhode, and H. B.

Liu, “New kinematic multi-section model for catheter contact force [165] A. Gupta, C. Eppner, S. Levine, and P. Abbeel, “Learning dexterous estimation and steering,” in Proc. IEEE/RSJ Int. Conf. Intelligent manipulation for a soft robotic hand from human demonstrations,” in Robots and Systems (IROS), Daejeon, Korea (South), 2016, pp. Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS), 2122–2127. Daejeon, Korea (South), 2016, pp. 3786–3793.

[146] H. Yuan, P. W. Y. Chiu, and Z. Li, “Shape-reconstruction-based force [166] J. Y. Nagase, S. Wakimoto, T. Satoh, N. Saga, and K. Suzumori, sensing method for continuum surgical robots with large deformation,” “Design of a variable-stiffness robotic hand using pneumatic soft IEEE Robot. Autom. Lett., vol. 2, no. 4, pp. 1972–1979, Oct. 2017. rubber actuators,” Smart Mater. Struct., vol. 20, Article No. 105015, Aug. 2011. [147] L. A. Huet, J. W. Rudnicki, and M. J. Z. Hartmann, “Tactile sensing

with whiskers of various shapes: Determining the three-dimensional [167] M. Manti, T. Hassan, G. Passetti, N. D’Elia, C. Laschi, and M. location of object contact based on mechanical signals at the whisker Cianchetti, “A bioinspired soft robotic gripper for adaptable and base,” Soft Robot., vol. 4, no. 2, pp. 88–102, Jun. 2017. effective grasping,” Soft Robot., vol. 2, no. 3, pp. 107–116, Sep. 2015.

[148] A. Bajo and N. Simaan, “Kinematics-based detection and localization [168] Y. She, C. Li, J. Cleary, and H. J. Su, “Design and fabrication of a soft of contacts along multisegment continuum robots,” IEEE Trans. robotic hand with embedded actuators and sensors,” J. Mech. Robot., Robot., vol. 28, no. 2, pp. 291–302, Apr. 2012. vol. 7, Article No. 021007, May 2015.

[149] A. Bajo and N. Simaan, “Finding lost wrenches: Using continuum [169] R. Deimel, M. Radke, and O. Brock, “Mass control of pneumatic soft robots for contact detection and estimation of contact location,” in continuum actuators with commodity components,” in Proc. IEEE/RSJ Proc. IEEE Int. Conf. Robotics and Autom., Anchorage, AK, USA, Int. Conf. Intelligent Robots and Systems (IROS), Daejeon, Korea 2010, pp. 3666–3673. (South), 2016, pp. 774–779.

[150] M. Khoshnam, A. C. Skanes, and R. V. Patel, “Modeling and [170] W. Wang and S. H. Ahn, “Shape memory alloy-based soft gripper with estimation of tip contact force for steerable ablation catheters,” IEEE variable stiffness for compliant and effective grasping,” Soft Robot., Trans. Biomed. Eng., vol. 62, no. 5, pp. 1404–1415, May 2015. vol. 4, no. 4, pp. 379–389, Dec. 2017.

[151] O. Khatib, L. Sentis, J. Park, and J. Warren, “Whole-body dynamic [171] S. Licht, E. Collins, M. L. Mendes, and C. Baxter, “Stronger at depth: behavior and control of human-like robots,” Int. J. Hum. Robot., vol. 1, Jamming grippers as deep sea sampling tools,” Soft Robotics, vol. 4, no. 1, pp. 29–43, Mar. 2004. no. 4, pp. 305–316, Dec. 2017.

[152] C. Della Santina, A. Bicchi, and D. Rus, “Dynamic control of soft [172] E. Steltz, A. Mozeika, J. Rembisz, N. Corson, and H. M. Jaeger, robots with internal constraints in the presence of obstacles,” in Proc. “Jamming as an enabling technology for soft robotics,” in Proc. SPIE IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS), Macau, 7642, Electroactive Polymer Actuators and Devices (EAPAD), San China, 2019, pp. 6622–6629. Diego, California, United States, 2010.

[153] V. Falkenhahn, A. Hildebrandt, R. Neumann, and O. Sawodny, [173] E. Brown, N. Rodenberg, J. Amend, A. Mozeika, E. Steltz, M. R. “Model-based feedforward position control of constant curvature Zakin, H. Lipson, and H. M. Jaeger, “Universal robotic gripper based continuum robots using feedback linearization,” in Proc. IEEE Int. on the jamming of granular material,” Proc. Natl. Acad. Sci. USA, Conf. Robotics and Autom. (ICRA), Seattle, WA, USA, 2015, pp. vol. 107, no. 44, pp. 18809–18814, Nov. 2010. 762–767. [174] Y. T. Li, Y. H. Chen, and Y. Q. Li, “Distributed design of passive

[154] F. Xu, H. S. Wang, W. D. Chen, and J. C. Wang, “Adaptive visual particle jamming based soft grippers,” in Proc. IEEE Int. Conf. Soft servoing control for an underwater soft robot,” Assembly Autom., Robotics (RoboSoft), Livorno, Italy, 2018, pp. 547–552. vol. 38, no. 5, pp. 669–677, Dec. 2018. [175] M. Brancadoro, M. Manti, S. Tognarelli, and M. Cianchetti,

[155] T. Wang, Y. C. Zhang, Z. Chen, and S. Q. Zhu, “Parameter “Preliminary experimental study on variable stiffness structures based identification and model-based nonlinear robust control of fluidic soft on fiber jamming for soft robots,” in Proc. IEEE Int. Conf. Soft bending actuators,” IEEE/ASME Trans. Mechatron., vol. 24, no. 3, Robotics (RoboSoft), Livorno, Italy, 2018, pp. 258–263. pp. 1346–1355, Jun. 2019. [176] J. Amend and H. Lipson, “The JamHand: Dexterous manipulation with

[156] X. C. Wang, T. Geng, Y. Elsayed, C. Saaj, and C. Lekakou, “A unified minimal actuation,” Soft Robot., vol. 4, no. 1, pp. 70–80, Mar. 2017. system identification approach for a class of pneumatically-driven soft [177] J. Nassour, V. Ghadiya, V. Hugel, and F. H. Hamker, “Design of new actuators,” Robot. Autonom. Syst., vol. 63, pp. 136–149, Jan. 2015. sensory soft hand: Combining air-pump actuation with superimposed

[157] Y. T. Li, Y. H. Chen, Y. Yang, and Y. Wei, “Passive particle jamming curvature and pressure sensors,” in Proc. IEEE Int. Conf. Soft Robotics and its stiffening of soft robotic grippers,” IEEE Trans. Robot., vol. 33, (RoboSoft), Livorno, Italy, 2018, pp. 164–169. no. 2, pp. 446–455, Apr. 2017. [178] R. Pfeifer, M. Lungarella, and F. Iida, “The challenges ahead for bio-

[158] R. Deimel and O. Brock, “A novel type of compliant and inspired 'Soft' robotics,” Commun. ACM, vol. 55, no. 11, pp. 76–87, underactuated robotic hand for dexterous grasping,” Int. J. Robot. Res., Nov. 2012. vol. 35, no. 1–3, pp. 161–185, Jan. 2016. [179] A. M. Nasab, A. Sabzehzar, M. Tatari, C. Majidi, and W. L. Shan, “A

[159] J. R. Amend, E. Brown, N. Rodenberg, H. M. Jaeger, and H. Lipson, soft gripper with rigidity tunable elastomer strips as ligaments,” Soft “A positive pressure universal gripper based on the jamming of Robot., vol. 4, no. 4, pp. 411–420, Dec. 2017. granular material,” IEEE Trans. Robot., vol. 28, no. 2, pp. 341–350, [180] W. Crooks, G. Vukasin, M. O’Sullivan, W. Messner, and C. Rogers, Apr. 2012. “Fin Ray ® effect inspired soft robotic gripper: From the robosoft

[160] P. Glick, S. A. Suresh, D. Ruffatto, M. Cutkosky, M. T. Tolley, and A. grand challenge toward optimization,” Front. Robot. AI, vol. 3, Article Parness, “A soft robotic gripper with gecko-inspired adhesive,” IEEE No. 70, Nov. 2016. Robot. Autom. Lett., vol. 3, no. 2, pp. 903–910, Apr. 2018. [181] O. Pfaff, S. Simeonov, I. Cirovic, and P. Stano, “Application of fin ray

[161] C. Tawk, A. Gillett, M. in het Panhuis, G. M. Spinks, and G. Alici, “A effect approach for production process automation,” Annals of 3D-printed omni-purpose soft gripper,” IEEE Trans. Robot., vol. 35, DAAAM & Proceedings, vol. 22, pp. 1247–1249, Jan. 2011. no. 5, pp. 1268–1275, Oct. 2019. [182] Y. Q. Li, Y. H. Chen, and Y. T. Li, “Pre-charged pneumatic soft

[162] P. Maeder-York, T. Clites, E. M. Boggs, R. A. Neff, P. Polygerinos, D. gripper with closed-loop control,” IEEE Robot. Autom. Lett., vol. 4, Holland, L. Stirling, K. C. Galloway, C. Wee, and C. J. Walsh, no. 2, pp. 1402–1408, Apr. 2019. “Biologically inspired soft robot for thumb rehabilitation,” J. Med. [183] D. R. Faria, P. Trindade, J. Lobo, and J. Dias, “Knowledge-based Devices, vol. 8, no. 2, Article No. 020934, Jun. 2014. reasoning from human grasp demonstrations for robot grasp

[163] F. Ilievski, A. D. Mazzeo, R. F. Shepherd, X. Chen, and G. M. synthesis,” Robot. Autonom. Syst., vol. 62, no. 6, pp. 794–817, Jun. XU AND WANG: SOFT ROBOTICS: MORPHOLOGY AND MORPHOLOGY-INSPIRED MOTION STRATEGY 1521

2014. [203] Y. T. Cao, Y. L. Liu, Y. L. Chen, L. L. Zhu, Y. Yan, and X. Chen, “A novel slithering locomotion mechanism for a snake-like soft robot,” J. [184] J. Fras, Y. Noh, M. Macias, H. Wurdemann, and K. Althoefer, “Bio- inspired octopus robot based on novel soft fluidic actuator,” in Proc. Mech. Phys. Solids, vol. 99, pp. 304–320, Feb. 2017.

IEEE Int. Conf. Robotics and Autom., Brisbane, QLD, Australia, 2018, [204] H. X. Guo, J. H. Zhang, T. Wang, Y. J. Li, J. Hong, and Y. Li, “Design pp. 1583–1588. and control of an inchworm-inspired soft robot with omega-arching locomotion,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA), [185] C. Christianson, N. N. Goldberg, D. D. Deheyn, S. Q. Cai, and M. T. Tolley, “Translucent soft robots driven by frameless fluid electrode Singapore, Singapore, 2017, pp. 4154–4159.

dielectric elastomer actuators,” Sci. Robot., vol. 3, no. 17, Article No. [205] G. Y. Gu, J. Zou, R. K. Zhao, X. H. Zhao, and X. Y. Zhu, “Soft wall- eaat1893, Apr. 2018. climbing robots,” Sci. Robot., vol. 3, no. 25, Article No. eaat2874, Dec. 2018. [186] B. Y. Liu and F. L. Hammond, “Modular platform for the exploration

of form-function relationships in soft swimming robots,” in Proc. 3rd [206] T. Umedachi and Y. Kawahara, “Caterpillar-inspired crawling robot IEEE Int. Conf. Soft Robotics (RoboSoft), New Haven, CT, USA, on a stick using active-release and passive-grip elastic legs,” in Proc. 2020, pp. 772–778. IEEE Int. Conf. Soft Robotics (RoboSoft), Livorno, Italy, 2018, pp. 461–466. [187] M. Ishida, D. Drotman, B. Shih, M. Hermes, M. Luhar, and M. T.

Tolley, “Morphing structure for changing hydrodynamic [207] Q. Y. Wu, V. Pradeep, and X. Y. Liu, “A paper-based wall-climbing characteristics of a soft underwater walking robot,” IEEE Robot. robot enabled by electrostatic adhesion,” in Proc. IEEE Int. Conf. Soft Autom. Lett., vol. 4, no. 4, pp. 4163–4169, Oct. 2019. Robotics (RoboSoft), Livorno, Italy, 2018, pp. 315–320.

[188] T. Li, K. Nakajima, M. Calisti, C. Laschi, and R. Pfeifer, “Octopus- [208] T. Umedachi, V. Vikas, and B. A. Trimmer, “Highly deformable 3-D inspired sensorimotor control of a multi-arm soft robot,” in Proc. IEEE printed soft robot generating inching and crawling locomotions with Int. Conf. Mechatronics and Autom., Chengdu, China, 2012, pp. variable friction legs,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots 948–955. and Systems, Tokyo, Japan, 2013, pp. 4590–4595.

[189] M. Calisti, M. Giorelli, G. Levy, B. Mazzolai, B. Hochner, C. Laschi, [209] J. S. Koh and K. J. Cho, “Omega-shaped inchworm-inspired crawling and P Dario, “An octopus-bioinspired solution to movement and robot with large-index-and-pitch (LIP) SMA spring actuators,” manipulation for soft robots,” Bioinspir. Biomim., vol. 6, no. 3, Article IEEE/ASME Trans. Mechatron., vol. 18, no. 2, pp. 419–429, Apr. 2013. No. 036002, Jun. 2011. [210] T. Umedachi and B. A. Trimmer, “Design of a 3D-printed soft robot

[190] M. Sfakiotakis, A. Kazakidi, and D. P. Tsakiris, “Octopus-inspired with posture and steering control,” in Proc. IEEE Int. Conf. Robotics multi-arm robotic swimming,” Bioinspir. Biomim., vol. 10, no. 3, and Autom. (ICRA), Hong Kong, China, 2014, pp. 2874–2879. Article No. 035005, May 2015. [211] H. Q. Niu, R. Y. Feng, Y. W. Xie, B. W. Jiang, Y. Z. Sheng, Y. Yu, H.

[191] F. G. Serchi, A. Arienti, I. Baldoli, and C. Laschi, “An elastic pulsed- X. Baoyin, and X. Y. Zeng, “MagWorm: A biomimetic magnet jet thruster for Soft Unmanned Underwater Vehicles,” in Proc. IEEE embedded worm-like soft robot,” Soft Robot., Aug. 2020. DOI: Int. Conf. Robotics and Autom., Karlsruhe, Germany, 2013, pp. 10.1089/soro.2019.0167. 5103–5110. [212] M. P. Nemitz, P. Mihaylov, T. W. Barraclough, D. Ross, and A. A.

[192] H. Ando, Y. Ambe, A. Ishii, M. Konyo, K. Tadakuma, S. Maruyama, Stokes, “Using voice coils to actuate modular soft robots: Wormbot, an and S. Tadokoro, “Aerial hose type robot by water jet for fire example,” Soft Robot., vol. 3, no. 4, pp. 198–204, Dec. 2016. fighting,” IEEE Robot. Autom. Lett., vol. 3, no. 2, pp. 1128–1135, Apr. [213] S. Rozen-Levy, W. Messner, and B. A. Trimmer, “The design and 2018. development of branch bot: A branch-crawling, caterpillar-inspired,

[193] F. Renda, F. Giorgio-Serchi, F. Boyer, and C. Laschi, “Locomotion soft robot,” Int. J. Robot. Res., vol. 40, no. 1, pp. 24–36, Jan. 2021. and elastodynamics model of an underwater shell-like soft robot,” in [214] J. Z. Ge, A. A. Calderón, and N. O. Pérez-Arancibia, “An earthworm- Proc. IEEE Int. Conf. Robotics and Autom., Seattle, WA, USA, 2015, inspired soft crawling robot controlled by friction,” in Proc. IEEE Int. pp. 1158–1165. Conf. Robotics and Biomimetics (ROBIO), Macau, China, 2017, pp.

[194] H. L. Liu, B. Taylor, and O. M. Curet, “Fin ray stiffness and fin 834–841. morphology control ribbon-fin-based propulsion,” Soft Robot., vol. 4, [215] E. F. M. Henke, S. Schlatter, and I. A. Anderson, “Soft dielectric no. 2, pp. 103–116, Jun. 2017. elastomer oscillators driving bioinspired robots,” Soft Robot., vol. 4,

[195] J. Shintake, H. Shea, and D. Floreano, “Biomimetic underwater robots no. 4, pp. 353–366, Dec. 2017. based on dielectric elastomer actuators,” in Proc. IEEE/RSJ Int. Conf. [216] M. S. Verma, A. Ainla, D. Yang, D. Harburg, and G. M. Whitesides, Intelligent Robots and Systems (IROS), Daejeon, Korea (South), 2016, “A soft tube-climbing robot,” Soft Robot., vol. 5, no. 2, pp. 133–137, pp. 4957–4962. Apr. 2018.

[196] T. D. Ta, T. Umedachi, and Y. Kawahara, “Inkjet printable actuators [217] J. Z. Ge, A. A. Calderón, L. L. Chang, and N. O. Pérez-Arancibia, “An and sensors for soft-bodied crawling robots,” in Proc. Int. Conf. earthworm-inspired friction-controlled soft robot capable of Robotics and Autom. (ICRA), Montreal, QC, Canada, 2019, pp. bidirectional locomotion,” Bioinspir. Biomim., vol. 14, no. 3, Article 3658–3664. No. 036004, Feb. 2019.

[197] B. Gamus, L. Salem, A. D. Gat, and Y. Or, “Understanding inchworm [218] J. H. Zhang, T. Wang, J. Wang, B. T. Li, J. Hong, J. X. J. Zhang, and crawling for soft-robotics,” IEEE Robot. Autom. Lett., vol. 5, no. 2, M. Y. Wang, “Dynamic modeling and simulation of inchworm pp. 1397–1404, Apr. 2020. movement towards bio-inspired soft robot design,” Bioinspir. Biomin.,

[198] D. Drotman, S. Jadhav, M. Karimi, P. De Zonia, and M. T. Tolley, vol. 14, no. 6, Article No. 066012, Sept. 2019. “3D printed soft actuators for a legged robot capable of navigating [219] J. O. Alcaide, L. Pearson, and M. E. Rentschler, “Design, modeling unstructured terrain,” in Proc. IEEE Int. Conf. Robotics and Autom. and control of a SMA-actuated biomimetic robot with novel functional (ICRA), Singapore, Singapore, 2017, pp. 5532–5538. skin,” in Proc. IEEE Int. Conf. Robotics and Autom. (ICRA),

[199] J. Rieffel, D. Knox, S. Smith, and B. Trimmer, “Growing and evolving Singapore, 2017, pp. 4338–4345. soft robots,” Artificial Life, vol. 20, no. 1, pp. 143–162, Winter. 2014. [220] A. A. Calderón, J. C. Ugalde, J. C. Zagal, and N. O. Pérez-Arancibia,

[200] R. Pfeifer and J. C. Bongard, How the Body Shapes the Way We Think: “Design, fabrication and control of a multi-material-multi-actuator soft A New View of Intelligence (A Bradford Book). Cambridge, MA, USA: robot inspired by burrowing worms,” in Proc. IEEE Int. Conf. MIT Press, 2006. Robotics and Biomimetics (ROBIO), Qingdao, China, 2016, pp. 31–38.

[201] F. Corucci, M. Calisti, H. Hauser, and C. Laschi, “Evolutionary [221] J. B. Wang, J. Min, Y. Q. Fei, and W. Pang, “Study on nonlinear discovery of self-stabilized dynamic gaits for a soft underwater legged crawling locomotion of modular differential drive soft robot,” robot,” in Proc. Int. Conf. Advanced Robotics (ICAR), Istanbul, Nonlinear Dyn., vol. 97, pp. 1107–1123, Jul. 2019. Turkey, 2015, pp. 337–344. [222] C. D. Onal and D. Rus, “Autonomous undulatory serpentine

[202] T. Umedachi, V. Vikas, and B. A. Trimmer, “Softworms: The design locomotion utilizing body dynamics of a fluidic soft robot,” Bioinspir. and control of non-pneumatic, 3d-printed, deformable robots,” Biomim., vol. 8, no. 2, Article No. 026003, Jun. 2013. Bioinspir. Biomim., vol. 11, no. 2, Article No. 025001, Mar. 2016. [223] M. Sitti, Mobile Microrobotics. Cambridge, Massachusetts: MIT Press, 1522 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 9, SEPTEMBER 2021

2017. robot,” IEEE Trans. Ind. Electron., vol. 64, no. 2, pp. 1737–1742, Feb. 2017. [224] X. M. Du, H. Q. Cui, T. T. Xu, C. Y. Huang, Y. L. Wang, Q. L. Zhao,

Y. S. Xu, and X. Y. Wu, “Reconfiguration, camouflage, and color- [239] S. Seok, C. D. Onal, K. J. Cho, R. J. Wood, D. Rus, and S. Kim, shifting for bioinspired adaptive hydrogel-based millirobots,” Adv. “Meshworm: A peristaltic soft robot with antagonistic nickel titanium Funct. Mater., vol. 30, no. 10, Article No. 1909202, Mar. 2020. coil actuators,” IEEE/ASME Trans. Mechatron., vol. 18, no. 5, pp. 1485–

[225] T. T. Xu, J. F. Yu, C. I. Vong, B. Wang, X. Y. Wu, and L. Zhang, 1497, Oct. 2013.

“Dynamic morphology and swimming properties of rotating miniature [240] T. T. Xu, G. Hwang, N. Andreff, and S. Régnier, “Planar path swimmers with soft tails,” IEEE/ASME Trans. Mechatron., vol. 24, following of 3-D steering scaled-up helical microswimmers,” IEEE no. 3, pp. 924–934, Jun. 2019. Trans. Robot., vol. 31, no. 1, pp. 117–127, Feb. 2015.

[226] B. J. Nelson, I. K. Kaliakatsos, and J. J. Abbott, “Microrobots for [241] C. Y. Huang, T. T. Xu, J. Liu, L. Manamanchaiyaporn, and X. Y. Wu, minimally invasive medicine,” Annu. Rev. Biomed. Eng., vol. 12, “Visual servoing of miniature magnetic film swimming robots for 3-D pp. 55–85, Aug. 2010. arbitrary path following,” IEEE Robot. Autom. Lett., vol. 4, no. 4,

[227] W. Q. Hu, G. Z. Lum, M. Mastrangeli, and M. Sitti, “Small-scale soft- pp. 4185–4191, Oct. 2019. bodied robot with multimodal locomotion,” Nature, vol. 554, no. 7690,

[242] A. Oulmas, N. Andreff, and S. Régnier, “3D closed-loop swimming at pp. 81–85, Feb. 2018. low Reynolds numbers,” Int. J. Robot. Res., vol. 37, no. 11, pp. 1359–

[228] H. Ceylan, J. Giltinan, K. Kozielski, and M. Sitti, “Mobile microrobots 1375, Sep. 2018. for bioengineering applications,” Lab Chip, vol. 17, pp. 1705–1724,

[243] F. Z. Low, J. H. Lim, and C. H. Yeow, “Design, characterisation and Apr. 2017. evaluation of a soft robotic sock device on healthy subjects for assisted

[229] S. Miyashita, S. Guitron, M. Ludersdorfer, C. R. Sung, and D. Rus, ankle rehabilitation,” J. Med. Eng. Technol., vol. 42, no. 1, pp. 26–34, “An untethered miniature origami robot that self-folds, walks, swims, Jan. 2018. and degrades,” in Proc. IEEE Int. Conf. Robotics and Autom., Seattle, WA, USA, 2015, pp. 1490–1496. [244] L. Mena, C. A. Monje, L. Nagua, J. Muñoz, and C. Balaguer, “Test bench for evaluation of a soft robotic link,” Front. Robot. AI, vol. 7, [230] Z. M. Liu, J. Q. Liu, H. Wang, X. Yu, K. Yang, W. B. Liu, S. L. Nie, Article No. 27, Mar. 2020. W. G. Sun, Z. X. Xie, B. H. Chen, S. Z. Liang, Y. C. Guan, and L.

Wen, “A 1 mm-thick miniatured mobile soft robot with mechanosen- [245] B. S. Homberg, R. K. Katzschmann, M. R. Dogar, and D. Rus, sation and multimodal locomotion,” IEEE Robot. Autom. Lett., vol. 5, “Robust proprioceptive grasping with a soft robot hand,” Auton. no. 2, pp. 3291–3298, Apr. 2020. Robot., vol. 43, pp. 681–696, Mar. 2019.

[231] H. W. Huang, M. S. Sakar, A. J. Petruska, S. Pané, and B. J. Nelson, “Soft micromachines with programmable motility and morphology,” Fan Xu (S’21) received the B.Eng. degree in new Nat. Commun., vol. 7, Article No. 12263, Jul. 2016. energy and science engineering from Huazhong

[232] H. Y. Chen, R. S. Diteesawat, A. Haynes, A. J. Partridge, M. F. University of Science and Technology, in 2015, the Simons, E. Werner, M. Garrad, J. Rossiter, and A. T. Conn, “RUBIC: M.S. degree in mechanical engineering in Arizona An untethered soft robot with discrete path following,” Front. Robot. State University, Tempe, USA, in 2016. Since 2017, AI, vol. 6, Article No. 52, Jul. 2019. she has been working toward the Ph.D. degree in control science and engineering in Shanghai Jiao

[233] S. Palagi, A. G. Mark, S. Y. Reigh, K. Melde, T. Qiu, H. Zeng, C. Parmeggiani, D. Martella, A. Sanchez-Castillo, N. Kapernaum, F. Tong University. Her research interests include soft Giesselmann, D. S. Wiersma, E. Lauga, and P. Fischer, “Structured robot and visual servoing. light enables biomimetic swimming and versatile locomotion of photo- responsive soft microrobots,” Nat. Mater., vol. 15, no. 6, pp. 647–653, Jun. 2016. Hesheng Wang (SM’15) received the B.Eng. degree

[234] C. L. Huang, J. A. Lv, X. J. Tian, Y. C. Wang, Y. L. Yu, and J. Liu, in electrical engineering from Harbin Institute of “Miniaturized swimming soft robot with complex movement actuated Technology in 2002, and the M.Phil. and Ph.D. and controlled by remote light signals,” Sci. Rep., vol. 5, Article No. degrees in automation and computer-aided 17414, Dec. 2015. engineering from The Chinese University of Hong Kong in 2004 and 2007, respectively. He is currently [235] J. R. Li, J. B. Wang, and Y. Q. Fei, “Nonlinear modeling on a SMA actuated circular soft robot with closed-loop control system,” a Professor with the Department of Automation, Nonlinear Dyn., vol. 96, pp. 2627–2635, Jun. 2019. Shanghai Jiao Tong University. His current research interests include visual servoing, service robot, [236] Z. Chen, S. Shatara, and X. B. Tan, “Modeling of biomimetic robotic computer vision, and autonomous driving. Dr. Wang fish propelled by an ionic polymer-metal composite caudal fin,” is an Associate Editor of IEEE Transactions on Automation Science and IEEE/ASME Trans. Mechatron., vol. 15, no. 3, pp. 448–459, Jun. 2010. Engineering, IEEE Robotics and Automation Letters, Assembly Automation

[237] M. Calisti, F. Corucci, A. Arienti, and C. Laschi, “Dynamics of and the International Journal of Humanoid Robotics, a Technical Editor of underwater legged locomotion: Modeling and experiments on an the IEEE/ASME Transactions on Mechatronics. He served as an Associate octopus-inspired robot,” Bioinspir. Biomim., vol. 10, no. 4, Article No. Editor of the IEEE Transactions on Robotics from 2015 to 2019. He was the 046012, Jul. 2015. General Chair of the IEEE RCAR 2016, and the Program Chair of the IEEE

[238] Y. Q. Fei and H. W. Xu, “Modeling and motion control of a soft ROBIO 2014 and IEEE/ASME AIM 2019.